PRACTICAL    THERMODYNAMICS 


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>T  IT  u  y  g  ir  IT  irif  t  ir  >T  a  ff  IT  g  irg  gju 


PRACTICAL  THERMODYNAMICS 


A  TREATISE  ON  THE  THEORY  AND  DESIGN  OF 
HEAT  ENGINES,  REFRIGERATION  MACHINERY, 
AND  OTHER  POWER-PLANT  APPARATUS 


BY 


FORREST  E.   CARDULLO,   M.E. 

MEMBER  OP   AMERICAN   SOCIETY  OF  MECHANICAL  ENGINEERS 

PROFESSOR  OF  MECHANICAL  ENGINEERING   IN    THE 
NEW   HAMPSHIRE   COLLEGE   OF   AGRICULTURE   AND  THE   MECHANIC   ARTS 


McGRAW-HILL    BOOK    COMPANY 

239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LONDON-,  E.G. 

1911 


COPYRIGHT,  1911 
BY 

MCGRAW-HILL  BOOK  COMPANY 


fHE    SCIENTIFIC    PRESS 
RT    DRUMMOND   AND    COMPANY 
BROOKLYN,    N.    Y. 


PREFACE 


IN  writing  this  volume  the  author  has  endeavored  to  present  the  natural 
laws  and  physical  principles  which  underlie  the  action  of  thermodynamic 
apparatus  in  such  a  manner  as  to  enable  the  student  not  only  to  compre- 
hend the  principles  upon  which  the  apparatus  depends  for  its  operation, 
but  also  to  assist  him  to  correctly  design  such  an  apparatus,  to  operate 
it,  and  to  judge  of  its  value. 

The  book  is  intended  primarily  as  a  text-book  for  the  use  of  junior 
and  senior  classes  in  mechanical  and  electrical  engineering.  It  there- 
fore attempts  to  present  the  subject  of  thermodynamics  from  the  physical 
rather  than  from  the  mathematical  standpoint.  While  the  treatment 
of  the  subject  is  rigorous,  a  minimum  of  higher  mathematics  is  used  and  the 
methods  employed  are  those  which  appeal  to  common  sense  rather  than 
to  a  knowledge  of  calculus.  The  writer  believes  that  the  higher  mathe- 
matics are  to  be  regarded  merely  as  a  set  of  tools  by  the  use  of  which  the 
engineer  may  accomplish  certain  results.  Hence  the  methods  employed 
in  developing  the  mathematical  part  of  the  work  depend  upon  the  objects 
to  be  accomplished,  and  are  the  simplest  and  most  effective  possible. 
They  are  usually  methods  which  lay  stress  on  the  physical  phenomena 
rather  than  those  which  appeal  to  the  accomplished  mathematician. 

The  writer  has  not  hesitated  to  present  new  methods  whenever  these 
methods  seem  to  be  simpler  and  better  than  the  older  ones.  Much  of 
the  difficulty  of  teaching  thermodynamics  arises  out  of  a  misunderstanding 
on  the  part  of  the  student,  of  the  phraseology  usually  employed,  and  from 
attempts  to  introduce  the  abstractions  of  the  ancient  philosophers  into 
the  concretions  of  modern  science.  Accordingly,  no  chapters  are  devoted 
to  the  first  or  second  laws  of  thermodynamics  and  no  puzzling  or  trouble- 
some analogies  are  offered  for  entropy.  Many  definitions  differ  radically 
from  those  offered  in  other  text-books,  but  the  changes  made  are  con- 
sidered advisable  in  order  to  make  the  presentation  of  the  subject  more 
logical  or  more  simple. 

It  does  not  seem  to  the  author  that  it  is  any  longer  necessary  or 
desirable  to  give  credit  to  the  originators  of  methods  of  thermodynamic 

267486 


vi  PREFACE 

investigation,  or  to  the  discoverers  of  physical  truths  long  known,  in  a 
work  of  this  kind.  Accordingly,  he  has  refrained  from  distracting  the 
student's  attention  by  continual  reference  to  names  which  are  strange 
to  him  and  which,  while  they  are  of  historic  interest,  should  have  no  place 
in  a  text-book.  While  this  book  contains  very  little  that  is  new,  and  is 
principally  a  presentation  of  truths  long  known,  yet  authorities  are  quoted 
but  seldom.  The  effect  of  such  references  and  quotations  upon  the 
student's  mind  is  usually  to  divert  his  thought  from  the  principles  to  be 
considered,  and  they  are  therefore  omitted  unless  some  unusally  good 
reason  dictates  their  insertion. 

The  author  has  separated  all  reference  to  the  temperature-entropy 
diagram  from  the  body  of  the  text  and  placed  it  it  a  separate  chapter 
(the  25th)  in  order  that  it  may  be  used  or  not  as  the  judgment  of  the 
teacher  shall  dictate.  The  material  in  the  25th  chapter  is  so  arranged 
that  it  exactly  parallels  the  remainder  of  the  book,  and  the  temperature- 
entropy  analysis  of  any  type  of  thermodynamic  machine  may  be  found 
in  its  proper  order.  It  is  the  author's  opinion  that  the  temperature- 
entropy  diagram  is  not  illuminating  to  the  average  student,  who  is  con- 
tinually seeking  for  some  physical  analogy  for  entropy  and  who  is 
continually  plunging  himself  into  difficulties  by  seeking  to  carry  his 
analogy  further  than  the  truth  will  warrant.  The  use  of  the  entropy 
function  in  developing  the  .theory  of  the  adiabatic  expansion  of  vapors, 
on  the  other  hand,  involves  no  difficulties  whatever,  and  the  author  has 
therefore  presented  this  matter  in  the  body  of  the  text. 

The  writer  has  attempted  at  all  times  to  bring  most  of  the  work  well 
within  the  comprehension  of  the  average  technical  student.  In  some 
places  it  will  seem  as  if  he  had  made  his  treatment  of  the  work  absurdly 
simple,  as,  for  instance,  in  the  description  of  the  steam  engine.  He 
believes,  however,  that  many  of  the  difficulties  encountered  by  students 
arise  from  a  misunderstanding  of  facts  which  seem  to  the  teacher  to  be 
perfectly  obvious  and  which  the  teacher  mistakenly  believes  that  the 
student  thoroughly  understands.  Another  difficulty  often  encountered 
in  teaching  thermodynamics  arises  from  the  fact  that  an  inadequate 
preparation  precedes  the  study  of  the  phenomena  of  heat  engines  and 
other  thermodynamic  machinery.  The  author  has  therefore  endeavored 
to  present  in  the  first  seven  chapters  of  the  book  the  fundamental  physical 
principles  upon  which  a  further  study  of  the  subject  must  depend,  in  such 
a  thorough  and  simple  manner  that  no  trouble  need  subsequently  arise 
from  a  misunderstanding  of  these  fundamentals. 

In  order  that  the  book  shall  be  available  to  the  largest  possible  num- 
ber of  classes,  the  author  has  included  many  items,  which,  while  they  are 
of  great  interest,  can  be  profitably  taught  only  to  advanced  students  or 
to  classes  in  which  the  amount  of  time  available  for  the  subject  is  greater 


PREFACE  vii 

than  that  usually  taken.  These  items  have  been  printed  in  smaller  type 
than  the  remainder  of  the  text,  and  the  teacher  can  omit  any  of  them  that 
he  may  see  fit,  without  omitting  any  of  the  essential  parts  of  the  work. 

The  problems  have  been  carefully  chosen  to  illustrate  the  principles 
treated  in  the  text.  The  author  believes  that  a  student  has  a  true  knowl- 
edge of  his  subject,  not  when  he  can  make  a  recitation  of  the  substance 
of  a  statement  in  a  text-book,  but  when  his  knowledge  can  be  applied  to 
the  solution  of  problems.  The  problems  have  been  so  arranged  as  to 
advance  the  student  one  step  at  a  time  in  his  work,  only  one  new  element 
being  introduced  in  each  problem.  By  concentrating  the  student's  atten- 
tion upon  the  new  element,  the  problems  are  made  more  easy  of  solution 
and  are  more  valuable  from  an  instructional  standpoint.  The  problems 
are  not  intended  as  examination  questions  to  show  the  student's  grasp 
of  his  subject,  but  are  rather  intended  to  be  suggestive  to  him  and  to  assist 
him  in  the  comprehension  of  the  text.  The  answers  accompany  the 
problems  in  each  case. 

In  working  the  problem  it  will  in  many  cases  be  necessary  to  make 
use  of  a  steam  table.  The  reader  should  therefore  procure  such  a  table. 
Either  Peabody's  tables,  published  by  John  Wiley  &  Sons,  or  Marks 
and  Davis'  tables,  published  by  Longmans,  Green  &  Co.,  will  be  found 
to  be  admirably  suited  for  the  work.  Peabody's  tables  are  preferable 
for  some  kinds  of  work,  while  Marks  and  Davis'  tables  will  be  found 
preferable  for  other  kinds.  All  the  values  given  in  the  book,  except 
those  specially  noted,  are  from  Marks  and  Davis'  tables. 

In  the  first  edition  of  any  work  of  this  character,  it  is  difficult  to  entirely 
eliminate  errors,  even  by  the  exercise  of  the  greatest  care.  Accordingly, 
the  author  will  be  very  grateful  to  any  of  his  readers  who  will  point  out 
to  him  errors  of  any  kind  which  he  may  find,  whether  in  the  statements 
made  or  in  the  answers  to  the  problems. 

In  conclusion  the  author  wishes  to  express  his  thanks  to  many  friends 
who  have  assisted  in  the  preparation  of  this  work,  particularly  Professors 
Charles  James,  L.  S.  Marks,  and  C.  H.  Peabody,  Dr.  William  Kent  and 
Mr.  Geo.  Orrok.  He  also  wishes  to  acknowledge  his  indebtedness  to 
the  firms  mentioned  on  page  x  for  material  furnished. 


ERRATA          ^ 

Page  7.  Fig.  1.     Ordinates  should  be  -0.20,  -0.10,  0.0,  +0.10,  +0.20. 

Page  11.  Prob.  3.     Ans.  3.2174.     Prob. /1 3 i  Ans.  13.998. 

Page  15.  In  equation  (4)  substitute  R  for  C'F.  not  for  C". 

Page  23.  Prob.  4.     Ans.  200.4. 

Page    36.     Last  expression  should  be  ~-j-  WP(V2-Vi). 

Page    37.     Equation  (2).     Insert  a  minus  sign  before  -5-. 

Page    38.     Art.  51.     P  in  equation  should  be  Pi. 

Page    46.     Equation  6.     Insert  brackets  after  ——  and  at  end. 

Page    49.     Prob.  16.     Ans.     123,000.     Prob.  18.     Ans.  25  and  510.     Prob. 

27.     Read  26  for  24. 
Page    50.     Prob.  40.     Ans.  0.809.     Prob.  41.     Ans.  0.0081.     Prob.  42.    Ans. 

0.0142.     Prob.  43.     Ans.  1.10. 
Page    57.     Line  3.     Read  4  for  3. 

Page    63.     Prob.  6.     Read  ft.-lbs.  for  B.T.U.    Prob.  15.     Ans.  42.8. 
Page    71.     Prob.  3.     Insert  161.1  in  ans.     Prob.  5.     Ans.  333.0.     Prob.  6. 

Ans.  .002851.     Prob.  9.     Ans.  798.1. 

Page    77.     In  paragraph  4,  line  2,  read  0.0886  and  so  in  line  5. 
Page    80.     In  equation  read  1.4094. 

Page    87.     Prob.    6.     Ans.  24.11.     Prob.    7.     Ans.  0.0415. 
Page    88.     Prob.  28.     Ans.  10,495.     Prob.  32.     Ans.  1.6020. 
Page    95.     Prob.    7.     Ans.  14.956. 

Page    96.     Prob.  16.     After  "  air  "  insert  "in  Problem  15." 
Page  108.     Second  line  from  bottom,  read  P'  for  P. 
Page  130.     In  second  equation  read  25.36  for  25.0. 

Page  139.     Prob.  4.     Ans.  25.4.     Prob.  5.     Ans.  26.6.     Prob.  6.     Ans.  1.064. 
Page  140.     Prob.  9.     Ans.  99.7.     Prob.  11.     Ans.  12.9.      Prob.  14.     Ans. 

122,800.     Prob.  15.     Ans.  15.7.     Prob.  17.     Cannot  be  solved 

since  compression  cannot  be  complete.     Prob.  18.     Cannot  be 

solved. 
Page  156.     Prob.  1.     Ans.  85.     Prob.  5.    Ans.  10.5.    Prob.  10.     Ans.  0.0276. 

Prob.  11.     Read  "cylinder"  for  "piston."     Ans.  19.6. 
Page  177.     Prob.  2.     Ans.  0.20  and  0.18.    Prob.  3.     Ans.  0.400  and  0.447. 

Prob.  9.     Assume  120  r.p.m.     Prob.  12.     Ans.  23,100. 
Page  185.     Inequations  at  bottom  of  page,  read  1.1778  for  1.1178.     Read 

0.964  for  96.4.     Read  1186.3  for  1183.3.     Read  7.40  for  7.45. 

Read  0.726  for  0.505. 
Page  198.     Prob.  5.     Read  17.9  for  16.9. 

(Over] 
CARDTJLLO'S  "PRACTICAL  THERMODYNAMICS." 


Page  214.     In  article  223,  paragraph  2,  line  8,  read  seventh  for  sixth,  ar 

in  line  9  read  sixth  for  seventh. 
Page  215.     In  col.  11  read  11.60  for  11.50,  in  col.  12  read  8.93  for  8.83  and  i 

col.  14  read  2.748  for  2.848  and  3.48  for  1.212. 
Page  217.     Sixth  line  from  bottom.     For  0.217  read  0.189.     Fourth  line  frc 

bottom.     For  3.792  read  3.683. 

Page  218.     Fourth  line.    Read  3940  for  3830.    Sixth  line.    Read  4030  for  3900. 
Art.  226.      Par.  2.     Line  6.    Equation  should  be  9X1052.3  =  9471.     Line  10. 

Equation   should  be   62,032-9471=52,562.     Line  12.     Read 

3500  for  3290.     Line  13.     Read  3570  for  3360. 
Page  219.     Par.  3.    Line  6.    Equation  should  be  62,032  XTV  =  4770.    Line  14. 

Read  18,170  for  18,250. 
Page  232.     Prob.  3.     Ans.  21.1.     Prob.  4.     Ans.  2560.    Prob.  6.    Ans.  2120. 

Prob.  7.     Line  2  read  CO  for  CO2. 
Page  233.     Prob.  19.     Ans.  2970. 
Page  251.     Prob.    7.     Ans.  60.3. 
Page  256.     Equation  6.     Read  .74  for  .75. 
Page  263.     Prob.    4.     Ans.  11.0. 
Page  273.     Prob.  7.     Ans.  3.83.      Prob.  8.      Ans.  1290.     Prob.  10.      Ans. 

15,100.     Prob.  11.     Ans.  3,130,000. 

Page  290.     Equation  (2).     For  ^y    read    |^. 

Page  295.     Line  11.     For  P  read  E. 

Page  301 .     Answers  contain  some  errors  in  third  significant  figure. 

Page  319.     Prob.  2.     Ans.  2.26.      Prob.  3.      Ans.  71,700.     Prob.  4.     Ans. 

1002.     Prob.   5.     Ans.   573.     Prob.   6.     Ans.  40.5.     Prob.   7. 

Ans.  232,500.     Prob.  8.     Ans.  160,800.     Prob.  9.     Ans.  13,660. 

Prob.  11.  Ans.  2.52. 
Page  343.  Prob.  2.  Ans.  41,400. 
Page  344.  Prob.  4.  Ans.  6900.  Prob.  5.  Ans.  8590.  Prob.  14.  Ans. 

0.0066.  Prob.  15.  Ans.  0.00503.  Prob.  16.  Ans.  503. 
Page  367.  Prob.  3.  An&.  32.5.  Prob.  5.  Ans.  45,150.  Prob.  6.  Ans. 

181.  Prob.  7.  Ans.  251.  Prob.  10.  Ans.  113. 

Page  369.     Third  line  from  bottom.     Read  isothermally  for  adiabatically. 
Page  371.     Second  line  from  bottom.     Read  b  —  c  for  b  —  d. 
Page  383.     Fifth  line  from  bottom.     Read  cdfg  for  idfg. 
Page  384.     Last  line  of  Art.  348.     Read  cdfg  for  idfg. 


CONTENTS 


.'TER  PAGE 

I.  INTRODUCTION.     THE  NATURE  AND  MEASUREMENT  OF  HEAT 1 

II.  THE  THERMAL  PROPERTIES  OF  GASES 12 

III.  THE  EXPANSION  OF  GASES 25 

IV.  THERMODYNAMIC  PROCESSES  AND  CYCLES 51 

V.  THE  THERMAL  PROPERTIES  OF  VAPORS 64 

VI.  WET  AND  SUPERHEATED  VAPORS 72 

VII.  MIXTURES  OF  GASES  AND  VAPORS 90 

VIII.  THE  STEAM  ENGINE 97 

IX.  STEAM  CYCLES v 125 

X.  LOSSES  IN  THE  STEAM  ENGINE 141 

XI.  NOTES  ON  THE  DESIGN  AND  TESTING  OF  STEAM  ENGINES 158 

XII.  THE  STEAM  TURBINE 178 

XIII.  CONDENSING  MACHINERY 199 

XIV.  COMBUSTION 214 

XV.  THE  STEAM  BOILER 234 

XVI.  BOILER  PLANT  AUXILIARIES 252 

XVII.  WATER-COOLING  APPARATUS 264 

XVIII.  HOT-AIR  ENGINES 274 

XIX.  THE  INTERNAL  COMBUSTION  ENGINE 285 

XX.  NOTES  ON  THE  DESIGN  AND  PERFORMANCE  OF  INTERNAL  COMBUSTION 

ENGINES 302 

XXI.  GASEOUS  FUELS 320 

XXII.  COMPRESSED  AIR 332 

XXIII.  REFRIGERATION 34f> 

XXIV.  HEATING,  VENTILATION,  EVAPORATION  AND  DRYING 356 

XXV.  ENTROPY  DIAGRAMS 368 

XXVI.  THE  KINETIC  THEORY  OF  HEAT 393 

ix 


ACKNOWLEDGMENTS 


The  author  is  indebted  to  the  following  firms  for  illustrations  and 
other  material  in  this  book. 

ALLIS-CHALMERS  Co. 

AMERICAN  ENGINE  Co. 

AMERICAN  LOCOMOTIVE  Co. 

CROSBY  STEAM  GAGE  AND  VALVE  Co. 

DE  LAVAL  TURBINE  Co. 

DIRECT  SEPARATOR  Co. 

FORE  EIVER  SHIPBUILDING  Co. 

GRAY  MOTOR  Co. 

HOLLY  MANUFACTURING  Co. 

MC-KENSIE  FURNACE  Co. 

NEW  YORK  ENGINE  Co. 

OHIO  BLOWER  Co. 

OTTO  GAS  ENGINE  Co. 

WESTINGHOUSE  MACHINE   Co, 

JOHN  WILEY  AND  SONS 


PRACTICAL  THERMODYNAMICS 


CHAPTER   I 
INTRODUCTION— THE   NATURE  AND   MEASUREMENT  OF  HEAT 

1.  The  Purpose  of  Thermodynamic  Machinery.     One  of  the  greatest, 
if  not  the  greatest,  of  our  engineering  problems,  is  the  transformation 
of  the  store  of  energy  with  which   Nature  is'  so  lavishly  endowed,  into 
those  forms  which  best  serve  the  purpose  of  mankind.     The  form  of 
energy  which  men  find  to  be  the  most  generally  useful  for  their  purposes 
is  that  form  which  we  term  work,  or  mechanical  energy.     Unfortunately, 
the  forms  in  which  energy  is  furnished  to  us  by  Nature   are  seldom 
those  which  are  immediately  available  to  our  purpose,  or  which  may 
be   transformed   into   work   by   simple   mechanical   appliances,   such   as 
windmills    or   water-wheels.      The    needs    of    society    are    usually   such 
that  mankind  is  commonly  obliged  to  avail  himself  of  that  vast  store 
of  natural  energy  found  in  the  form  of  potential  chemical  energy  in 
combustible  substances.     This  form  of  energy  can  be  liberated,  so  far 
as  we  know,  only  in  the  form  of  heat.     In  order  to  make  Nature's 
store  of  energy  of  use  to  us,  therefore,  it  is  necessary  first  to  transform 
it  into  the  form  of  heat,  and  then  in  most  cases  to  transform  this  heat 
into  some  more  useful  form  of  energy,  such  as  work,  or  electricity,  or 
light.     In  doing  so,  we  make  use  of  certain  forms  of  engineering  apparatus 
which  we  may  term  thermodynamic  machines. 

Thermodynamics,  in  the  sense  in  which  it  is  used  by  physicists,  is 
that  branch  of  physical  science  which  treats  of  the  effects  produced 
by  heat  and  the  phenomena  accompanying  their  various  manifestations. 
When  used  by  the  engineer,  however,  the  term  thermodynamics  is 
understood  to  mean  that  branch  of  engineering  science  which  deals  with 
the  interconversion  of  heat  and  work,  and  the  phenomena  attendant 
thereon. 

2.  The  Conservation  and  Correlation  of  Energy.     One  of  the  funda- 
mental axioms  of  physical  science  is  that  the  sum  total  of  the  energy 


2         THE  NATURE  AND  MEASUREMENT  OF  HEAT     ART.  5 

of  the  universe  is  a  constant  quantity  and  that  this  energy  may  not  be 
increased  or  diminished,  created  or  destroyed,  by  any  known  process 
or  power.  This  physical  axiom,  known  as  the  doctrine  of  the  con- 
servation of  energy,  lies  at  the  basis  of  our  theory  of  thermodynamics. 
As  a  corollary  of  the  axiom  of  the  conservation  of  energy,  we  may  state 
that  the  different  forms  of  energy  are  mutually  inter-convertible,  and 
that  the  amount  of  one  form  of  energy  which  will  be  required  to  produce 
a  given  amount  of  any  other  form  of  energy  is  fixed  and  invariable. 
For  instance  we  find  that  a  certain  quantity  of  work  will  invariably  be 
transformed  into  a  certain  quantity  of  heat,  that  a  certain  quantity  of 
electrical  energy  is  the  equivalent  of  a  definite  quantity  of  potential 
chemical  energy,  and  so  on  throughout  the  entire  list  of  possible  con- 
versions. 

3.  Standards    of    Measurement.     Fundamental    Units.      As    a    pre- 
liminary to  the  intelligent  discussion  of  any  engineering  subject,  it  is 
necessary    to'  establish    certain    standards    of    measurement.     Without 
such  standards  it  is  impossible  to  express  quantitative  relations,  or  to 
make  of  the  physical  sciences  anything  but  an  orderly  array  of  curious 
and    interesting,    but    generally   useless,    facts.     If   these    standards    of 
measurement   are  to   be   of  value   in  engineering  work,   they   must  be 
those  which  society  uses  in  its  ordinary  dealings,  and  with  which  man- 
kind generally,  and  workmen  more  particularly,  are  thoroughly  familiar. 
Accordingly,    engineers    in    English-speaking    countries    use    as    their 
standards  of  measurement  those  units  which  are  collectively  known  as 
the  Foot  Pound  Second  system.     This  system,  while  not  so  elaborate, 
or  perhaps  so  rational,  as  the  C.G.S.  system  in  use  among  physicists, 
has  the  immense  practical  advantage  that  its  units  are  understood  by 
everyone,  and  are  those  in  common  use  in  our  workshops. 

4.  Length.     The  unit  of  length  is  the  foot  which  is  defined  1  as  0.30480 
meter  or  30.48  centimeters.     The  meter  is  defined  as  the  length  of  a 
certain   bar   of   metal,    accepted    as   the   standard  of   length   by   inter- 
national agreement.     The  centimeter,  which  is  the  standard  of  length 
used  in  physical  measurements,  is  Vioo  part  of  the  length  of  this  bar. 
In  certain  engineering  work  the  inch  is  a  unit  of  length.     The  inch  is, 
however,    never   used    in    rational    energy    equations.     The    symbol    of 
length  is  L. 

5.  Mass.     The  unit  of  mass,  or  quantity  of  matter,  is  the  pound, 
which  is  defined  l  as  0.453592  kilogram,  or  453.592  grams.      A  kilogram 
is   the    mass    contained   in    a   certain    metal   weight,   accepted    as    the 
standard  of  mass  by  international  agreement.     The  gram  is  Viooo  part 
of    the  kilogram.      The  symbol  of  mass,  when   expressed   in    pounds, 
is  W. 

1  By  Act  of  Congress. 


ART.  6  UNITS  OF  MEASUREMENT  3 

6.  Time.    The  unit   of  time  is  the  mean  solar  second,  invariably 
called  simply  the  second  (except  in  works  on  astronomy) ,  which  is  1/8Q4oo 
part  of  the  mean  solar  day.     The  symbol  of  time  is  t. 

7.  Force.     The  unit  of  force  is  the  weight  of  1  pound,  or  the  force 
with  which  the  earth  attracts  a  mass  of    1  pound,  at  any  point  where 
the  acceleration  produced  by  gravitation  is  32.1740  feet  per  second  per 
second.1     For  convenience  and  brevity,  the  unit  of  force  is  also  known 
as  a  pound.     The  symbol  of  force  is  F. 

8.  Relation  between  Force,  Mass,  and  Acceleration.     It  will  be  noted  that 
the  unit  of  force  (1  pound)  does  not  produce  an  acceleration  of  1  foot  per  second 
per  second,   in  the  unit  of  mass  (1   pound).     In  consequence  of    this    fact,  in  all 
kinetic  energy  equations  we  use  for  the  unit  of  mass  that  quantity  of  matter  to 
which  the  unit  of  force  does  give  an  acceleration  of  1  foot  per  second  per  second. 
This  quantity  of  matter  is  32.1740  pounds  and  is  usually  termed  the  kinetic  mass  unit. 
The  symbol  for  mass,  when  expressed  in  kinetic  mass  units,  is  M ,  which  is,  of  course, 

W 
equal  to  — . 

00 

9.  Derived  Units.     From  the  four  fundamental  units  of  length,  mass, 
time,    and    force,   the    following    units    of     measurement    are    directly 
derived: 

10.  Area.    The  unit  of  area  is  the  square  foot.     In  practical  engi- 
neering calculations  the  square  inch,  which  is,  of  course,  Yi44  part  of 
the  square  foot,  is  generally  used  as  the  unit  of  area.     The  symbol  for 
area  is  A. 

11.  Volume.    The  unit  of  volume  is  the  cubic  foot.     The  symbol 
for  volume  is  V. 

12.  Work,  or  Energy.    The  unit  of  work,  and  therefore  the  funda- 
mental unit  of  energy,  is  the  foot-pound,  which  is  the  quantity  of  work 
performed  by  a  force  of   1   pound  in  moving  its  point  of  application 
through  a  distance  of    1    foot,  measured  in    the    direction  of    its    line 
of    action.      The    symbol  for  energy,  when  expressed  in  foot-pounds, 
is  U. 

13.  Power.     Power  is  the  rate  of  doing  work,  or  the  rate  of  expendi- 
ture of  energy.     The  practical  unit  of  power  is  the  horse-power,  which 
is  equivalent  to  the  performance  of  work  at  the  rate  of  550  foot-pounds 
per   second.     The   symbol   for  power,   when   measured   in  horse-power, 
is  H.P. 

14.  Pressure.     Intensity    of   pressure,    called    for   brevity,    pressure, 
is  the  rate  of  application  of  a  uniformly  distributed  force  upon  an  area, 

1  This  value  for  the  acceleration  of  gravity  has  been  accepted  as  standard  by 
international  agreement.  The  symbol  for  the  acceleration  produced  by  gravity  is 
g.  and  for  the  value  32.1740  the  symbol  g0  may  be  used. 


4          THE  NATURE  AND  MEASUREMENT  OF  HEAT     ART.  16 

and  is  found  by  dividing  the  total  force  by  the  total  area  upon  which 
it  is  applied.  The  units  of  pressure  are  four  in  number.  The  first  is 
the  pressure  of  1  pound  per  square  foot.  This  is  the  unit  of  pressure 
employed  in  all  rational  thermodynamic  equations.  The  second  is  the 
pressure  of  1  pound  per  square  inch,  which  is  144  times  as  great 
as  the  first.  This  is  the  unit  employed  in  engineering  tables,  such  as 
steam  tables,  and  so  on,  and  in  engineering  calculations.  The  third  is 
the  pressure  produced  by  a  column  of  pure  mercury  1  inch  high,  at 
a  temperature  of  32°  F.,  when  g  is  32.1740  feet  per  second  per  second. 
This  is  the  unit  generally  used  in  condenser  and  gas  calculations.  The 
fourth  is  the  normal  pressure  of  the  atmosphere  at  sea  level,  which  has 
been  defined  by  international  agreement  to  be  the  pressure  produced 
by  a  column  of  pure  mercury  29.921  inches  high,  at  a  temperature  of 
32°  F.  where  g  is  32.1740  feet  per  second  per  second.  This  unit  of 
pressure  is  termed  an  atmosphere.  The  symbol  for  pressure,  when 
expressed  in  pounds  per  square  foot,  is  P. 

15.  Absolute    and    Gage    Pressure.     Pressure   gages  of  the  type   or- 
dinarily used   in  engineering   work   do  not   measure    the  true  pressure 
exerted  upon  their  mechanism,  but  the  excess  of  this  pressure  over  that 
of  the  atmosphere.     The  pressure  recorded  by  such  an  instrument  is 
called  the  gage  pressure,  and  may  be  reduced  to  the  true  or  absolute 
pressure  by  adding  the  actual  pressure  of  the  atmosphere  as  deduced 
from  the  barometer  reading.     In  like  manner,  a  vacuum  gage  registers 
the  amount  by  which  a  pressure  falls  short  of  that  of  the  atmosphere 
and  the  "  vacuum  "  so  recorded  may  be  reduced  to  absolute  pressure 
expressed  in  inches  of  mercury,  by  subtracting  it  from  the  reading  of 
the    barometer.     Unless    pressures    are    stated    to    be    gage  pressures, 
they   are   understood   to   be   absolute    pressures,   in   works   of  thermo- 
dynamics. 

16.  Effects  of  Heat.    Energy  itself  cannot  be  perceived.     We  may 
only  perceive  and  measure  it  by  the  effects  which  it  produces.     Heat, 
being  a  form  of  energy,   can  only  be  perceived  and    measured  by  its 
effects.     We  term  a  body  hot  or  cold  according  to  the  effects  which  we 
feel  when  we  are  in  contact  with  it  or  in  its  neighborhood.     We  find  that 
hot  bodies  tend  to  give  up  heat  to  cold  bodies,  and  eventually  all  attain 
the  same  degree  of  warmth,  when  they  are  brought  near  one  another. 
When  one  body  is  capable  of  giving  up  heat  to  another  body  we  say 
that  the  first   body  has  a  higher    temperature    than    the    second.     As 
a    result   of    heat    exchange  between   bodies    of    different  temperatures 
(i.e.,  the  addition  of   heat  to  cold  bodies  and  the  abstraction  of  heat 
from  hot  bodies),  we  find  that  some  or  all  of  the  following  effects  are 
produced. 

First,  the  addition  of    heat  to  a  body  almost  always  increases  its 


ART.  17  THE   MEASUREMENT  OF  TEMPERATURE  5 

temperature,  making  it  more  capable  of  giving  up  heat  to  colder  bodies, 
and  less  capable  of  absorbing  heat  from  hotter  bodies.  The  rise  in 
temperature  is  usually  very  nearly  proportional  to  the  quantity  of  heat 
added.  Second,  the  addition  of  heat  to  a  body,  with  consequent  rise 
in  temperature,  generally  tends  to  expand  that  body,  and  the  amount 
of  the  expansion  is  usually  very  nearly  proportional  to  the  quantity 
of  heat  added.  Third,  the  addition  of  heat  to  a  body,  with  conse- 
quent rise  in  temperature,  quite  often  results  in  a  change  in  the 
physical  state  of  the  body.  For  instance,  the  addition  of  heat  to  ice 
changes  it  into  water;  the  addition  of  heat  to  water  changes  it  to 
steam. 

The  abstraction  of  heat  has  in  each  of  the  above  cases  the  contrary 
effect,  reducing  the  temperature,  decreasing  the  volume,  and  changing 
the  physical  state  from  that  of  a  gas  or  liquid  to  that  of  a  liquid  or 
solid.  For  instance,  the  abstraction  of  heat  from  carbon  dioxide,  which 
is  a  gas,  reduces  its  temperature  and  volume,  and  finally  changes  it  to 
a  snow-like  solid. 

The  addition  of  heat  to  certain  kinds  of  bodies  results  in  a  change 
in  their  chemical  composition.  For  instance,  the  addition  of  heat  to 
potassium  chlorate,  KC1O3,  changes  it  to  potassium  chloride  and  oxygen, 
the  formula  for  the  reaction  being  2KC1O3  =  2KC1+3O2.  Such  phe- 
nomena, however,  unlike  the  ones  recorded  in  the  preceding  paragraph, 
are  not  usually  reversible.  Subsequent  abstraction  of  heat  will  not 
return  such  substances  to  their  original  chemical  form. 

In  all  of  these  cases,  the  amount  of  change  produced,  as  measured 
by  the  quantity  of  material  changed,  is  always  proportional  to  the 
amount  of  heat  producing  the  change,  so  that  heat  may  be,  and  is, 
measured  quantitatively  by  scientists,  by  means  of  the  physical  effects 
which  it  produces. 

17.  The  "Measurement  of  Temperature.  Since  the  most  obvious 
change  ordinarily  produced  in  a  body  by  the  addition  or  abstraction 
of  heat  is  the  elevation  or  depression  of  its  temperature,  we  must  first 
seek  some  suitable  method  of  measuring  temperature.  It  has  been 
found  that  ice  melts  at  a  certain  definite  temperature,  provided  that 
the  ice  be  formed  from  pure  water,  and  the  fusion  occurs  at  a  pressure 
of  one  atmosphere.  This  temperature  is  known  in  physics  as  the  ice- 
point.  It  is  also  known  that  the  temperature  of  the  steam  which  comes 
from  boiling  water  at  a  pressure  of  one  atmosphere  is  a  fixed  quantity. 
This  temperature  is  known  in  physics  as  the  boiling-point.  If  we  may 
find  some  method  of  determining  the  temperature  of  a  body  with 
reference  to  these  two  points,  we  will  have  a  system  of  thermometry, 
or  temperature  measurement. 

We  have  noted  that  one  of  the  effects  of  heat  is  to  expand  almost 


6         THE  NATURE  AND  MEASUREMENT  OF  HEAT     ART.  18 

all  bodies  to  which  it  is  added.  Gases  expand  to  a  greater  degree  upon 
the  addition  of  heat  than  do  any  other  substances,  and  are  therefore 
better  suited  than  other  substances  to  the  purposes  of  exact  ther- 
mometry.  Some  gases  expand  with  great  regularity,  the  amount  of 
expansion  so  produced  being  strictly  proportional  to  the  quantity  of 
heat  producing  the  expansion  and  giving  a  definite  measure  of  the  rise 
in  temperature  of  the  gas.  Helium  and  hydrogen  are  such  gases. 
Other  gases,  such  as  air,  oxygen,  etc.,  while  often  used  in  thermometry, 
are  less  regular  in  their  rate  of  expansion.  Still  other  gases,  such  as 
carbon  dioxide,  are  so  irregular  in  their  rate  of  expansion  as  to  be  quite 
unsuited  for  the  purposes  of  thermometry.  It  is  therefore  the  custom 
among  physicists,  as  a  result  of  international  agreement,  to  adopt  for 
the  measurement  of  temperature  the  indications  of  a  hydrogen  ther- 
mometer.1 The  method  of  construction  and  use  of  such  a  standard 
thermometer  is  described  in  Art.  31.  The  symbol  of  temperature  is  T. 
(See  Art.  26.) 

18.  Thermometer  Scales.  In  engineering  work  in  English-speaking 
countries  the  Fahrenheit  thermometer  scale  is  in  common  use.  One 
degree  on  the  Fahrenheit  scale  is  defined  as  YIRO  part  of  the  rise  in 
temperature,  as  indicated  by  a  standard  hydrogen  thermometer,  from 
the  ice-point  to  the  boiling-point.  The  Fahrenheit  zero  is  32°  below 
the  melting-point  of  ice,  so  that  the  temperature  of  the  ice-point  is 
32°  Fahrenheit  (generally  written  32°  F.)  and  the  temperature  of  the 
boiling-point  is  212°  F.  In  countries  using  the  metric  system,  and  in 
purely  scientific  work,  the  centigrade  thermometer  scale  is  used.  The 
centigrade  degree  is  Yioo  part  of  the  rise  in  temperature  from  the 
ice-point  to  the  boiling-point.  The  centigrade  zero  is  the  ice-point 
and  the  centigrade  temperature  of  the  boiling-point  is  100°  (generally 
written  100°  C.). 

In  order  to  reduce  Centigrade  to  Fahrenheit  temperatures,  we  may 
make  use  of  the  formula 


(1) 


In  order  to  reduce  Fahrenheit  to  Centigrade  temperatures,  we  may 
make  use  of  the  formula 

-  32) 


9 


1  For  reasons  of  convenience,  it  is  not  the  volume  of  the  hydrogen,  but  the  pressure 
which  it  exerts  upon  the  walls  of  the  bulb  in  which  it  is  confined  at  constant  volume, 
which  affords  a  measure  of  its  temperature. 


ART.  19 


THE   BRITISH   THERMAL   UNIT 


In  these  formula?,  C  and  F  are  respectively  corresponding  Centigrade 
and  Fahrenheit  temperatures. 

19.  Mercury  Thermometers.  For  the  ordinary  measurement  of  temperature 
in  engineering  work,  "mercury  in  glass"  thermometers  are  used.  The  indications  of  a 
perfect  thermometer  of  this  type,  (i.e.,  one  filled  with  pure  mercury,  and  having  a  capil- 
lary tube  of  absolutely  uniform  bore)  depend  upon  the  kind  of  glass  from  which  it  is 
made,  and  the  conditions  under  which  it  is  used,  and  are  invariably  different  from 
those  of  the  hydrogen  thermometer,  except  at  the  ice-point  and  boiling-point.  Such 
thermometers  are,  however,  sufficiently  exact  for  most  engineering  work,  although 
entirely  unsatisfactory  for  refined  investigations,  unless  suitably  handled  and 
calibrated.  In  Fig.  1  will  be  found  a  graphical  representation  of  the  errors  of  a  perfect 
mercury  in  glass  thermometer  at  different  temperatures.  It  will  be  seen  that  the 
error  is  so  small  as  not  to  be  important  in  ordinary  engineering  work. 


4-20 


-1-10 


-20 


'0     20     40     60     80     100    120    140    160    180   200    220  240    260   280    300   320   340    360   380    400 
Fahrenheit  Temperature  by  Mercury  Thermometer 

JTIG>    i — Correction    curve  to    reduce  mercury  in    glass    thermometer    readings    to 
hydrogen  therm.ometer  readings. 

20.  The  British  Thermal  Unit.    Temperature  measures  intensity  of 
heat,  or  in  other  words,  it  determines  the  ability  of  a  body  to  surrender 
heat  to,   or   abstract   it   from,   a  body   of   a  different  temperature.     It 
does  not,  however,  tell  us  the  amount  of  heat  which  the  body  contains. 
In  order  to  measure  quantity  of  heat,  we  need  another  unit  of  measure- 
ment aside  from  that  of  temperature.     The  unit  of  measurement  used  in 
engineering    calculations    in    English-speaking    countries    is   termed   the 
Mean  British  Thermal  Unit,  and  may  be  denned  as  Viso  part  of  the 
heat  required  to  raise  1  pound    of   pure  water  from    a  temperature  of 
32°  F.  to  a  temperature  of  212°  F.  (i.e.,  from  the  ice-point  to  the  boiling- 
point)   without  loss  of  mass,  under  a  pressure  of  one  atmosphere.     In 
order  to  avoid  the  use  of  the  cumbersome  term  Mean  British  Thermal 
Unit,  the  symbol  B.T.U.  is  used.    The  symbol  for  quantity  of  heat  is  H. 

21.  The    Mechanical    Equivalent    of  Heat.       Since  heat    is    a    form 
of  energy   and  the   different   forms   of  energy   are   inter-convertible,   it 
follows  that  work  may  be  converted  into  heat.     As  a  result  of  a  long 
series   of  experiments   carried   out   by   many   different   men   at   various 
times,   it   has  been  shown  that   777.5  ±    foot-pounds  of  work  may  be 
transformed    into    one    B.T.U.     This    quantity,    777.5    foot-pounds,    is 


8  THE   NATURE  AND   MEASUREMENT  OF  HEAT       ART.  22 

known  as  the  mechanical  equivalent  of  heat,  and  in  thermodynamic 
equations,  we  use  for  its  exact  (but  unknown)  value,  the  symbol  J. 

22.  Specific  Heat.  If  a  small  quantity  of  heat  be  added  to  a  substance 
without  changing  its  physical  or  chemical  state,  its  temperature  will  be 
somewhat  increased.  The  rise  in  temperature  produced  will  be  directly 
proportional  to  the  quantity  of  heat  absorbed,  and  inversely  propor- 
tional to  the  mass  absorbing  it.  The  proportionality  factor,  which 
varies  widely  for  different  substances,  is  known  as  the  specific  heat  of 
the  substance.  The  specific  heat  of  a  substance  may  be  defined  as  the 
number  of  B.T.U.  required  to  raise  the  temperature  of  1  pound  of 
the  substance  1°  F.  It  follows  from  the  definition  of  the  Mean 
British  Thermal  Unit,  and  that  of  specific  heat,  that  the  average  specific 
heat  of  water  between  the  temperature  of  32°  and  212°  F.  is  unity. 
The  term  average  is  used,  because  it  has  been  found  that  the  specific 
heat  of  different  substances,  water  included,  is  not  a  constant  quantity, 
but  depends  upon  the  temperature  of  the  substance.  Therefore,  in 
physical  or  engineering  investigations  requiring  great  exactitude,  account 
must  be  taken  of  this  variation  in  the  specific  heat  of  substances, 
although  in  ordinary  engineering  work  it  is  not  necessary  to  do  so. 

Tables  are  appended  showing  the  relation  of  the  English,  the  Metric, 
the  Electrical  Engineering,  and  the  C.G.S.  systems  of  units,  used  in 
engineering  and  physical  measurements. 


TABLE  I 
LENGTH 


Feet. 

Inches. 

Meters. 

Centimeters. 

Foot               

1 

12 

0.30480 

30.48000 

Inch 

0  08333 

1 

0.02540 

2.54001 

Meter                      

3.28083 

39.37996 

1 

100 

Centimeter 

0  032808 

0  39380 

0  01 

1 

Millimeter  

0.003281 

0.03938 

0.001 

0.1 

TABLE  II 
AREA 


Sq. 

Feet. 

Inches. 

Meters. 

Centimeters. 

Foot                                   .    ... 

1 

144 

0  .  092903 

929.03 

Inch 

0  0006944 

1 

0  00064516 

6  4516 

Meter                            

10.7639 

1550  0 

1 

10,000 

Centimeter 

0.00107639 

0  15500 

0  0001 

1 

ART.  22 


TABLES  OF  EQUIVALENT  UNITS 


TABLE  III 
VOLUME 


Cubic. 

Feet. 

Inches. 

Yards. 

Meters. 

Liters. 

Centimeters. 

Foot  

1 

1728 

.037038 

.028317 

28.317 

28317 

Inch  

.0005787 

1 

.000021433 

.000016387 

.016387 

16.387 

Yard.....  . 

27 

46,656 

1 

.  76454 

764  .  54 

764.540 

Meter  

35.314 

61,023 

1.3081 

1 

1000 

1,000,000 

Liter  

.035314 

61.023 

.001308 

.001 

1 

1000 

Centimeter 

.000035314 

.061023 

.  00000  130S 

.000001 

.001 

1 

TABLE  IV 

MASS 


. 

Pounds. 

Kilograms. 

Grams. 

Pound 

1 

0  453592 

453  592 

Kilogram  
Gram 

2.04622 
0  00204622 

1 

0  001 

1000 
1 

TABLE  V 
FORCE 


Pounds. 

Kilogram. 

Dyne. 

Pound 

1 

0.453592 

444,800 

Kilogram       

2  .  04622 

1 

980,665 

Dyne 

0  0000020866 

0.00000101975 

1 

10 


THE  NATURE  AND  MEASUREMENT  OF  HEAT 


ART.  22 


si 


"§"5 


?££si"ii 

D    T*    CO        •    S   rH 


CO  C^  ^^          HH 
rH  <N  O          to 


CO  »O  CO  CO 
•  (N  l>  t-» 

o 


CO         tO  O 

eOi  i— ( 
tO  O 
co  o 


t^.   O   CO    rH  O 

000  O 

odd  o 


o  o 


CO   ^ 
•  O 


i—  i       c^  10 

,_,   05   05 


° 


rH  CO    (N    O 

.  r^  co  oo  QO 

•  rH    T^    r^, 

O  rH    O         • 

I>-  (N  (M  <N 


O 


tO 

HH    ^    OS    (M    CO    rH 

O  5  CD  (N  CO  O 

o  do 


w 
J 
pq 

<j 

EH 


Is 

§1 


Kilogr 
mete 


III. 


0  0  0  0  0 


(N 

CO 


0  0  0  C    0 


<M  O  "*  CO  to  I> 

co  o  co  S3     •     • 

O  <N  O  O  00  CD 

o  o  o  o 


TH  CO 

CD         (M          oo 

s^gsss 

S     8§8 


tO  CO   O   t^-       ix  ^ 

•  CO       •  CO  to  o" 


s 


18 


PROBS.  1-23  PROBLEMS  U 

PROBLEMS 

1.  With  what  force  does  the  earth  attract  a  mass  of  1   lb.,  at  a  point  where  the 
acceleration  produced  by  gravity  is  32.1500  ft.  per  sec.?  Ans.  IO'ITAQ  lbs' 

2.  Find  the  acceleration  of  gravitation  at  a  point    where   a  mass  of    1    ton   is 
attracted  by  the  earth  with  a  force  of  2001.5  Ibs.  Ans.    32.1981  ft.  per  sec.2 

3.  What  acceleration  will  a  force  of  1  lb.  impart  to  a  mass»of  10  Ibs.? 

Ans.    3.1274  ft.  per  sec.2 

4.  What  acceleration  will  a  force  of  1  lb.  impart  to  a  body  whose  mass  is  2  kinetic 
mass  units?  Ans.    0.5  ft.  per  sec.2 

5.  What  will  be  the  weight  of  a  kinetic  mass  unit  at  a  point  where  the  acceleration 
of  gravitation  is  32.1600  feet  per  sec.2?  Ans.    32.16  Ibs. 

6.  A  piston  is  10  his.  in  diameter.     Find  its  area.  Ans.    0.5454  sq.ft. 

7.  A  box  is  18  ins.  wide,  24  ins/  long,  and  12  ins.  deep.     What  is  its  volume? 

ATJ.S.    3  cu.ft. 

8.  What  work  is  performed  in  raising  a  mass  of  100  Ibs.  a  vertical  distance  of  10 

feet  at  a  point  where  g = 32.100.  Ans.    ^4^1  =  997.7  ft.-lbs. 

oJ.174 

9.  WThat  power  is  required  to  raise  a  mass  of  one  ton  with  a  velocity  of  5£  feet 
per  second,  where  g  =  32. 1740?  Ans.    20  H.P. 

10.  The  weight  of  a  cubic  inch  of  ice-cold  mercury  is  0.491170  lb.     What  pres- 
sure in  pounds  per  square  inch  equals  10  ins.  of  mercury  (correction  for  variation  in 
the  force  of  gravity  omitted)?  Ans.    4.9117  Ibs.  per  sq.in. 

11.  What  is  the  value  of  an  atmosphere  in  pounds  per  square  inch? 

Ans.    14.696  Ibs.  per  sq.in. 

12.  What  in  pounds  per  square  foot?  Ans.    2116.3  Ibs.  per  sq.ft. 

13.  A  pressure  gage  reads  60  Ibs.  when  the  pressure  of  the  air  is  14.5  Ibs.  per 
square  inch.     What  is  the  absolute  pressure?  Ans.    74.5  Ibs,  per  sq.in. 

14.  The  barometer  reads  28.5  ins.     What  is  the  absolute  pressure  of  the  air? 

Ans.    14.007  Ibs.  per  sq.in.  1 

15.  What  is  the  absolute  pressure  in  a  condenser  when  a  vacuum  gage  attached 
to  it  reads  26  ins.  with  the  barometer  as  in  Problem  14? 

Ans.    2.5  ins.  =  1.229  Ibs.  per  sq.in. 

16.  The  temperature  of  a  body  is  50°  F.     Find  its  Centigrade  temperature. 

Ans.    10°  C. 

17.  The  temperature  of  a  body  is  20°  C.     Find  its  Fahrenheit  temperature. 

Ans.    68°  F. 

18.  A  mercury  thermometer  indicates  a  temperature  of  60°.     What  is  the  tem- 
perature by  the  hydrogen  thermometer?  Ans.    60.12°  F. 

19.  What  quantity  of  heat  will    be    required  to  raise    1    ton  of   water  from  the 
ice-point  to  the  boiling-point.  Ans.    360,000  B.T.U. 

20.  What  is  the  mechanical  equivalent  of  10  B.T.U.?  Ans.    7775  ft.-lbs. 

21.  1000  ft.-lbs.  of  work  are  the  equivalent  of  what  quantity  of  heat? 

Ans.    1.2850  B.T.U. 

22.  A  body  weighing  3.5  Ibs.  is  raised  4°  in  temperature  by  the  expenditure  of  7 
B.T.U.     Find  the  specific  heat.  Ans.    0.5. 

23.  A  body  weighing  20  Ibs.  and  having  a  specific  heat  of  0.700  is  raised  10°  in 
temperature.     What  quantity  of  heat  is  absorbed?  Ans.    140  B.T.U. 


CHAPTER  II 


THE  THERMAL  PROPERTIES   OF   GASES 

23.  The  States  of  Matter.  All  substances  may  be  classified  accord- 
ing to  their  physical  state  as  solid  or  fluid.  Solid  substances  are  those 
which  are  not  permanently  deformed  by  slight  forces  and  which  there- 
fore retain  their  form  when  they  are  unconfined.  Fluids  are  those 
substances  which  flow,  that  is,  which  have  no  definite  form  except  that 
which  is  imposed  upon  them  by  the  containing  vessel.  Fluids  are 
classified  as  elastic  and  inelastic.  Inelastic  fluids  or  liquids,  are  those 
which  are  practically  incompressible,  and  therefore  do  not  change 
appreciably  in  volume  or  density  under  varying  pressures.  Elastic 

fluids  are  in  turn  divided  into  vapors  and 
gases.  Vapors  are  those  elastic  fluids 
which  are  readily  transformed  into  liquids 
by  a  slight  reduction  in  temperature. 
Gases  are  those  elastic  fluids  which  re- 
quire a  considerable  reduction  in  tem- 
perature to  reduce  them  to  the  form 
of  liquids.  As  an  example  of  these 
various  physical  states,  we  may  cite  iron 
as  a  solid,  water  as  a  liquid,  steam  as  a 
vapor,  and  air  as  a  gas. 

24.  The  Relation  between  the  Pressure 
and  Volume  of  a  Mass  of  Gas.  Let  us 
assume  that  we  have  a  receiver  whose 
construction  is  such  that  we  may  vary 
its  volume  at  will,  and  that  it  contains 
-a  quantity  of  air.  Such  a  receiver  is 
shown  in  Fig.  2.  This  imaginary  appa- 
ratus consists  of  a  cylinder  about  13  \ 

inches  in  internal  diameter  and  having 
FIG.  2-Ideal  apparatus  for  the  cross.gectional  area  of  j  e  foot 

.  ... 

It  is  flat   bottomed,  and   sliding  within 

it  there  is  a  gas-tight  piston  without 
weight,  which  works  smoothly  up  and  down,  without  friction.  Weights 
may  be  placed  on  the  piston  and  the  amount  of  weight  in  pounds  so 

12 


o 


1000 


Pisto 


1  cu.  ft. 
Air 


° 


^ 


investigation  of  the  properties  of 


ART.  24  PRESSURE  AND  VOLUME  OF  A   MASS  OF  GAS  13 

placed,  will  obviously  be  the  pressure  of  the  confined  gas,  expressed  in 
pounds  per  square  foot.  The  distance  between  the  bottom  and  the  flat 
face  of  the  piston,  in  feet,  is  equal  to  the  volume  of  the  confined  gas, 
in  cubic  feet.  The  pressure  of  the  air  is  removed  from  the  top  of  the 
piston  by  a  suitable  air-pump.  Let  us  assume  that  this  receiver  is  sur- 
rounded by  melting  ice  so  that  its  temperature  and  that  of  its  contents 
is  kept  at  32°  F.  Let  us  assume  also  that  the  quantity  of  air  which  the 
receiver  contains  is  such  that  when  its  volume  is  exactly  1  cubic  foot 
(i.e.,  when  the  piston  is  1  foot  from  the  bottom)  its  pressure,  measured 
above  an  absolute  vacuum  by  the  weights  placed  upon  the  piston,  will 
be  exactly  1000  pounds  per  square  foot.  If  now  we  place  2000  pounds 
upon  the  piston,  it  will  be  forced  downward  until  the  volume  of  the 
confined  air  becomes  J  a  cubic  foot.  If  the  weight  upon  the  piston 
be  made  500  pounds,  the  piston  will  rise  until  the  volume  of  the 
confined  air  becomes  2  cubic  feet,  and  if  the  weight  be  made  333  J 
pounds,  the  volume  will  increase  to  3  cubic  feet. 

»  An  inspection  of  the  foregoing  figures  will  serve  to  show  that  the 
product  of  the  pressure  and  volume  is  always  1000  foot-pounds.  No 
matter  how  the  pressure  may  be  altered,  the  volume  will  so  adjust  itself 
that  it  will  be  inversely  proportional  to  the  pressure,  and  as  long  as  no 
air  enters,  or  escapes  from,  the  receiver,  and  the  temperature  remains 
at  32°  F.,  the  product  of  the  pressure  and  the  volume  will  remain 
constant.  We  may  express  this  mathematically  by  the  equation 


where  P  is  the  pressure  of  a  confined  mass  of  air  at  a  temperature  of  32°  F.; 
V  is  the  corresponding  volume  of  this  mass  of  air; 
PO  is  the  original  pressure  of  the  same  mass  of  air,  at  the  same  tem- 

perature ; 
FQ  is  the  original  volume. 

The  above  statement  is  subject  to  modification  at  very  high  pres- 
sures. All  gases,  air  included,  when  sufficiently  compressed  and  cooled, 
are  changed  first  into  vapors  and  then  into  liquids,  in  which  states  they 
behave  in  a  very  different  manner.  Therefore,  when  a  gas  is  compressed 
to  such  a  degree  that  it  becomes  a  vapor,  or  its  volume  begins  to 
approach  the  volume  of  the  liquid  into  which  it  would  condense,  it  no 
longer  conforms  to  the  above  law,  but  its  behavior  approximates  that 
of  a  vapor  or  a  liquid. 

Had  we  taken  another  gas  instead  of  air  —  hydrogen,  for  instance— 
we  would  have  found  exactly  the  same  relation  between  the  volume 
and  the  pressure,  provided  we  started  with  one  cubic  foot  of  gas  at  a 
pressure  of  1000  pounds  per  square  foot.  No  matter  what  the  gas  with 


14  THE  THERMAL  PROPERTIES  OF   GASES  ART.  26 

which  we  experiment,  so  long  as  the  temperature  be  kept  constant  at 
32°  F.,  if  the  product  of  the  pressure  and  volume  be  initially  1000  foot- 
pounds, this  product  will  remain  1000  foot-pounds,  no  matter  what  we 
may  subsequently  make  the  volume  or  the  pressure.  The  mathe- 
matical expression  for  the  relation  of  the  pressure  and  volume  of  any 
gas  at  a  constant  temperature  is  therefore  the  same  as  that  already 
given  for  air,  namely, 

PV=P0V0. 

This  law  is  known  in  physics  as  Boyle's  law. 

25.  The  Relation  between  the  Pressure,  Volume,  and  Temperature  of 
a  Mass  of  Gas.     Let  us  now  see  what  effect  will  be  produced  upon  the 
pressure  of  a  given  mass  of  gas,  confined  in  a  given  volume,  by  a  change 
in  its  temperature.     Consider  again  the  ideal  apparatus  already  described, 
containing  1   cubic  foot  of  air  at  a  pressure  of   1000  pounds  per  square 
foot  and  a  temperature  of  32°  F.     If  we  raise  the  temperature  of  this 
mass  of  air  while  we  keep  the  volume   constant,  its  pressure  will  be 
found  to  increase.     When  the  temperature  has  been  raised  by  491.6° 
(i.e.,  until  it  becomes  523.6°  F.)  the  pressure  will  be  increased  by  1000 
pounds,    becoming    2000    pounds    per    square    foot.     Upon    raising   the 
temperature   another  491.6°,  to   1015.2°   F.,  the  pressure   will  increase 
another  thousand  pounds,  rising  to  3000  pounds  per  square  foot.     If  by 
some    means   we    depress   the   temperature   to    213.8°   below   zero,    the 
pressure  will  fall  to  500  pounds  per  square  foot. 

26.  The  Absolute  Zero.     It  will  be  apparent  from  the  above  facts 
that  the  rate  of  pressure  increase  or  decrease,  under  the  above  circum- 
stances,  is    1000   pounds   per   square   foot   for   each  491.6°   increase   or 
decrease    of   temperature.     Since   the   pressure   is   by   hypothesis,    1000 
pounds  per  square  foot  at  32°  F.,   at  a  temperature  491.6°  lower,   or 
—  459.6°,   the  pressure   will    become   zero.      Had  the   original    pressure 
at  32°  F.  been  P  pounds  per  square  foot,  the  increase  or  decrease  would 
have  been  found  to  be  P  pounds  per  square  foot  for  every  491.6°  increase 
or  decrease  of  temperature,  and  the  pressure  would  have  become  zero 
at  —459.6°,  no  matter  what  the  value  of  P  might  have  been  at  32°  F. 

The  fact  that  the  product  of  the  pressure  and  volume  of  a  gas  tends, 
in  theory  at  least,  to  become  zero  at  —459.6°,  led  physicists  to  infer  that 
a  body  having  this  temperature  would  be  devoid  of  heat  energy,  and 
therefore  could  not  possibly  have  a  lower  temperature.  Many  other 
phenomena  have  since  been  noted,  which  point  to  the  same  conclusion, 
so  that  this  temperature  has  become  known  in  physics  and  thermo- 
dynamics as  absolute  zero.  The  absolute  temperature  of  a  body  is  then 
its  temperature  measured  above  absolute  zero,  and  is  found  by  adding 
459.6°  to  the  Fahrenheit  temperature.  (In  case  the  absolute  tern- 


ART.  27  THE  CHARACTERISTIC  EQUATION  OF  GASES  15 

perature  is  wanted  in  Centigrade  degrees,  add  273.1°  to  the  Centigrade 
temperature.) 

The  lowest  temperature  which  has  been  actually  obtained  is  -457°  F.,  which 
is  about  3°  absolute.  At  this  temperature  all  known  gases  become  liquid  at  ordinary 
pressures,  and  most  of  them  solidify.  Metals  become  intensely  brittle,  and  also 
almost  perfect  conductors  of  electricity.  Many  strange  magnetic,  electrical,  and 
chemical  phenomena  are  noted.  This  temperature  was  obtained  by  the  condensa- 
tion of  helium  at  high  pressure,  and  its  subsequent  evaporation  under  an  air-pump. 

27.  The  Characteristic  Equation  of  Gases.  An  inspection  of  the 
figures  given  in  Art.  26  shows  that  the  pressure  of  a  mass  of  gas  confined 
within  a  constant  volume  is  proportional  to  the  absolute  temperature 
of  the  gas.  We  may  express  this  fact  mathematically  by  the  equation, 

P  =  C'T, (1) 

where  P  is  the  pressure  of  the  gas, 

T  is  the  absolute  temperature,  and 

C1  is  a  constant  depending  on  the  composition,  mass,  and  volume  of 
the  gas. 

Let  us  assume  that  the  mass  of  the  gas  is  1  pound.  Multiplying 
both  sides  of  equation  (1)  by  V  we  have 

PV  =  C'VT, (2) 

where  V  is  the  volume  in  which  the  pound  of  gas  is  confined.  Now 
since  by  hypothesis  the  gas  is  maintained  at  constant  volume,  we  may 
write 

C'V  =  R, (3) 

where  R  is  a  constant  independent  of  T,  since  both  C'  and  V  are  constants. 
Substituting  R  for  C'  we  have 

PV  =  RT, (4) 

for  1  pound  of  any  gas  at  a  constant  volume.  Now  it  has  already 
been  shown  in  Art.  24  that  when  T  is  a  constant  the  product  PV  is  also 
a  constant.  Therefore  the  value  of  R  for  any  gas  is  a  constant,  and  is 
independent  of  the  value  of  V  or  P  as  well  as  of  T. 

Since  the  mass  of  a  quantity  of  gas  at  a  given  pressure  and  tem- 
perature is  proportional  to  its  volume,  it  follows  that  the  equation 
relating  the  pressure,  temperature,  volume,  and  mass  of  a  quantity  of 
gas  may  be  written 

PV=WRT,  . (5) 


16  THE   THERMAL   PROPERTIES   OF   GASES  ART.  28 

where  P  =  the  absolute  pressure  of  the  gas  in  pounds  per  sq.ft.; 
V  =  the  volume  of  the  gas  in  cubic  feet  ; 
W  =  the    mass    (or    weight)    in    pounds    of    the    quantity  of  gas 

considered  ; 
T  =  the  absolute  temperature  of  the  gas,  on  the  Fahrenheit  scale, 

found  by  adding  459.6°  to  the  Fahrenheit  temperature  of  the 

gas;  and 
/2  =  a   constant    depending   upon   the   density   of   the    gas.     (The 

density  depends  on  the  chemical  constitution  of  the  gas,  i.e., 

on  the  quantity  and  molecular  weight  of  its  constituents.) 

28.  Perfect  Gases.     A  gas  whose  properties  are  such  that  it  fulfills 
exactly  the  relation 

PV=W  RT, 

at  all  temperatures  and  pressures,  is  called  a  perfect  gas.  It  is  now 
known  that  no  gases  are  perfect  in  this  sense.  However,  at  ordinary 
temperatures  (i.e.,  from  —100°  to  +600°  F.)  and  at  pressures  of  less 
than  ten  atmospheres,  the  irregularities  in  behavior  of  such  gases  as 
hydrogen,  helium,  etc.,  are  so  inconsiderable  as  to  be  detected  only  by 
the  most  refined  physical  measurements,  and  such  gases  are  therefore 
said  to  be  sensibly  perfect  under  such  conditions.  Practically  all  gases 
are  so  nearly  perfect  that  they  may  be  considered  perfect  gases  in 
engineering  computations. 

A  quantity  of  gas  having  a  definite  pressure,  temperature,  volume, 
and  mass  is  said  to  have  a  definite  thermodynamic  state  which  is  defined 
by  these  quantities.  It  will  be  noted  that  there  are  four  quantities 
upon  which  the  state  of  a  gas  depends,  and  if  three  of  them  are  known, 
the  fourth  may  be  found.  The  expression 

PV=WRT 

defines  the  relation  of  these  quantities  which  determine  the  state  of  the 
gas. 

29.  A  Second  Form  of  the  Characteristic  Equation.     If  we  assume 
that  a  certain  mass  of  gas  has  a  pressure  P0,  a  volume  of   F(),  and  a 
temperature  T0,  we  may  write 


WRTo  .........     (1) 

Transposing,  this  may  be  written 


ART.  30       VALUE  OF  R   IN   THE   CHARACTERISTIC   EQUATION  17 

If  this  quantity  of  gas  suffers  a  change  of  state,  and,  as  a  result, 
assumes  a  pressure  P,  a  volume  V,  and  a  temperature  T,  we  may  of 
course  write 

PV  =  WRT,     . (3) 

and  therefore  by  transposition, 

P  V 

-~  =WR (4) 

Combining  equations  (2)  and  (4)  we  have 

~T      "V2 ® 

This  equation  is  often  more  convenient  to  use  than  the  equation 
developed  in  Art.  27.  So  long  as  P  and  P(),  V  and  V0,  and  T  and  T0 
are  in  the  same  units,  they  may  be  units  of  any  convenient  size.  For 
instance,  we  may,  in  using  this  expression,  measure  pressures  in  milli- 
meters of  mercury,  volumes  in  liters,  and  temperatures  in  Centigrade 
degrees  on  the  absolute  scale.  So  long  as  the  same  units  are  employed 
throughout  the  equation,  it  makes  no  difference  what  these  units  may  be. 

30.  Value  of  R  in  the  Characteristic  Equation.  Since  at  given  pressures 
and  temperatures,  different  gases  have  different  densities  (i.e.,  weights  per  cubic 
foot),  it  follows  that  their  volumes  per  pound  and  therefore  the  value  of  R  found 
from  the  expression 

R  =  W~T' 

will  differ,  the  value  of  R  being  inversely  proportional  to  the  density,  and  therefore 
to  the  molecular  weight  of  the  gas. 

The  best  value  for  the  density  of  the  air  free  from  water  vapor  and  carbon 
dioxide,  as  given  by  Traverse,  from  Moreley,  Rayleigh,  and  Leduc,  is  1.29284 
grams  per  liter,  at  32°  F.  under  a  pressure  of  one  atmosphere.  Reducing  to  the 
F.P.S.  system  we  find  this  to  be  0.080710  pounds  per  cubic  foot.  Since  one  atmos- 
phere equals  2116.3  pounds  per  square  foot,  we  may  write  in  the  expression 

PV  =  WRT, 

2116.3  Xl=  0.080710  XRX  491. 60 
and 

R  =  53.338  for  air. 

The  density  of  oxygen  is,  from  the  same  authority,  1.42900  grams  per  liter. 
Since  the  function  R  varies  inversely  as  the  density  of  the  gas,  we  will  find  R  for 
oxygen  to  be 

R=53.338xi||jj|=48.256. 


18  '  THE  THERMAL   PROPERTIES   OF   GASES  ART.  31 

The  molecular  weight  of  oxygen  gas  is  32.  The  value  of  the  function  R  for 
oxygen,  as  we  have  just  seen,  is  48.256.  Since  the  value  of  R  is  inversely  proportional 
to  the  molecular  weight  of  any  gas,  which  we  may  designate  by  the  symbol  M,  we 
may  write 

48.256       M 
R  32' 

from  whence  ^48.256X33 

M 


From  the  above  equations  it  may  be  seen  that  the  value  of  R  for  any  gas  of 
known  chemical  composition  may  be  found  by  dividing  1544.2  by  the  molecular 
weight  of  the  gas.  Thus  the  molecular  weight  of  CO2  is  44.  Hence  the  value  of  R 
for  CO2  is  1544-^-44=35.11.  If  the  molecular  weight  of  the  gas  is  unknown,  but 
the  density,  as  compared  with  that  of  air,  is  known,  the  value  of  R  may  be  found 
by  dividing  53.338  by  the  density  of  the  gas.  Thus  the  density  of  CO2  is  1.5207 
whence  the  value  of  R  is  53.338-^1.520  =  35.11. 

For  the  density,  value  of  R,  and  other  thermodynamic  properties  of  the  principal 
gases,  see  Table  VIII  on  page  23. 

31.  Gas  Thermometers.  The  gas  thermometer  depends  upon  the 
principle  that  the  product  of  the  pressure  and  volume  of  a  sensibly 
perfect  gas  is  proportional  to  its  absolute  temperature.  Air,  nitrogen, 
helium,  and  hydrogen  are  the  gases  usually  employed  in  such  instru- 
ments. The  thermometers  are  of  two  types,  first  those  in  which  the 
gas  is  confined  within  a  bulb  having  a  definite  volume,  and  the  tem- 
perature is  measured  by  measuring  the  pressure  exerted  by  the  gas, 
and  second,  those  in  which  the  gas  is  confined  under  constant  pressure 
and  the  temperature  is  measured  by  finding  the  amount  of  expansion 
or  contraction  which  the  gas  undergoes.  It  has  been  found  that 
hydrogen  and  helium  are  the  two  gases  which  give  the  best  results  when 
used  as  thermometric  fluids,  and  there  seems  to  be  no  difference  in 
behavior  which  would  indicate  that  one  was  better  than  the  other. 
Accordingly,  physicists  have  adopted  for  the  standard  of  temperature 
measurement  a  constant  volume  hydrogen  thermometer,  in  which  the 
gas  is  confined  at  a  pressure  of  1000  millimeters  of  mercury  when  its 
temperature  is  zero  Centigrade. 

Such  a  thermometer  is  shown  in  principle  in  Fig.  3.  In  this  drawing,  A  is  a  bulb 
of  glass,  fused  quartz,  or  other  suitable  material,  in  which  the  gas  is  confined.  To 
this  bulb  is  sealed  a  capillary  tube  B,  in  which  the  mercury  may  be  made  to  rise  by 
means  of  the  reservoir  R  connected  to  B  by  the  rubber  tube  C.  The  tube  D,  from  the 
top  of  which  the  air  has  been  exhausted,  is  also  connected  to  B,  and  acts  as  a  baro- 
metric tube.  The  difference  between  the  level  of  the  mercury  in  the  reservoir  and 


ART.  32 


THE   SPECIFIC   HEATS  OF   GASES 


19 


in  the  tube  D  will,  of  course,  be  the  barometric  pressure  of  the  atmosphere.     The 
difference  in  level  between  the  mercury  in  the  capillary  tube  and  in  the  tube  D  will 
be  the  absolute  pressure  of  the  gas  confined  in  bulb  A,  which 
will  be  sensibly  proportional  to  the  absolute  temperature  of 
this  gas. 

In  using  the  instrument,  the  bulb  A  is  immersed  in  a 
bath  whose  temperature  is  to  be  measured.  The  reservoir 
R  is  elevated  until  the  mercury  is  brought  to  a  definite 
point,  which  is  marked  on  the  capillary  tube.  The  difference 
in  level,  I,  is  then  read  by  means  of  a  cathetometer  or  some 
similar  instrument.  Allowances  must,  of  course,  be  made 
for  the  thermal  expansion  of  the  material  of  the  bulb,  for 
the  fact  that  the  gas  in  the  capillary  tube  B  is  not  of  the 
same  temperature  as  the  gas  in  the  bulb,  for  the  expansion, 
or  contraction,  of  the  bulb  produced  by  the  difference  in 
pressure  of  the  bath  in  which  it  is  immersed  and  the  gas 
which  it  contains,  for  the  density  of  the  mercury  column, 
which  is  affected  by  its  temperature,  and  for  the  value  of 
the  gravitational  constant  at  the  place  where  the  measure- 
ment is  made. 

32.  The  Specific  Heats  of  Gases.  When  a  gas 
is  heated  the  amount  of  heat  required  is  found  to 
depend,  as  in  all  other  substances,  upon  the  rise 
in  temperature  and  upon  the  quantity  of  gas 
heated.  Since  an  unconfined  mass  of  .gas  does  not 
occupy  a  definite  volume,  we  may  have  two  con- 
ditions under  which  a  mass  of  gas  may  be  heated. 

i  n       i        -,i  .  T    n    ',  i    FIG.    3. — Diagrammatic 

It  may   be   confined   within   a  definite  space  and      sketch  of  a%onstant 

heated  at   constant  volume,  or  it  may  be  confined      volume  thermometer, 
under  a  definite  pressure  and  allowed  to  expand  as 

it  is  heated.  In  case  the  gas  is  confined  at  constant  volume,  the  increase 
of  pressure  resulting  from  the  addition  of  heat  does  not,  of  course, 
perform  work.  When,  however,  the  gas  is  confined  at  constant  pressure, 
and  allowed  to  expand  as  it  is  heated,  work  is  performed.  It  is  found 
that  the  amount  of  heat  required  to  raise  1  pound  of  a  gas  1°  in 
temperature  differs  under  these  two  circumstances,  being  greater  when 
the  gas  is  heated  at  constant  pressure  than  when  it  is  heated  at  constant 
volume.  Theory  indicates,  and  experiment  shows,  that  the  excess  of 
heat  required  in  the  former  case  is  equal  to  the  amount  of  work  done 
by  the  gas  in  expanding  at  constant  pressure. 

The  specific  heat  of  a  substance  has  already  been  defined  as  the 
number  of  B.T.U.  required  to  raise  1  pound  of  the  substance  1°  F.  in 
temperature.  In  this  definition  nothing  was  said  about  pressure,  but 
the  pressure  was  tacitly  assumed  to  be  a  constant  pressure  of  one 
atmosphere.  Since  all  substances  expand  somewhat  on  heating,  it 
follows  that  a  certain  amount  of  the  heat  applied  to  any  substance, 


20  THE  THERMAL  PROPERTIES  OF   GASES  ART.  33 

under  such  conditions,  is  transformed  into  work,  when  the  substance 
expands  against  atmospheric  pressure.  Since,  however,  the  amount  of 
expansion  of  most  substances  is  very  small,  the  amount  of  work  so 
done  is  also  exceedingly  small.  In  the  case  of  iron,  the  amount  of  work 
done  amounts  to  about  0.00009  per  cent  of  the  heat  required,  or  the 
result  is  affected  by  nine  parts  4n  ten  million.  In  the  case  of  a  gas, 
however,  the  increase  in  volume  produced  by  heating  is  very  consider- 
able as  compared  with  that  produced  in  other  substances,  and  therefore 
we  are  obliged  to  consider  a  gas  as  having  two  specific  heats,  one  at 
constant  pressure,  and  the  other  at  constant  volume. 

The  specific  heat  of  a  gas  at  constant  pressure  is,  of  course,  the 
number  of  B.T.U.  required  to  raise  the  temperature  of  1  pound  of 
it  1°  F.  at  any  constant  pressure.  This  quantity  is  found  to  be  inde- 
pendent of  the  amount  of  the  pressure,  so  long  as  the  pressure  remains 
constant.  The  symbol  for  the  specific  heat  of  the  gas  at  constant 
pressure  is  Cp.  The  specific  heat  of  a  gas  at  constant  volume  is  the 
number  of  B.T.U.  required  to  raise  the  temperature  of  1  pound  of 
the  gas  1°  F.  at  constant  volume.  The  symbol  for  the  specific  heat 
at  constant  volume  is  Cv.  The  specific  heat  at  constant  pressure  is 
equal  to  the  specific  heat  at  constant  volume  plus  the  heat  equivalent 
of  the  work  done  by  1  pound  of  the  gas  in  expanding  at  constant 
pressure  while  rising  1°  in  temperature. 

We  may  also  express  the  specific  heat  of  a  gas  in  dynamic  units 
(i.e.,  in  foot-pounds).  The  specific  heat  of  a  substance  in  dynamic 
units  is  the  number  of  foot-pounds  required  to  raise  its  temperature 
1°  F.,  and  is,  of  course,  equal  to  777.5  times  its  specific  heat  in  B.T.U. 
per  pound.  The  symbol  for  the  dynamic  specific  heat  of  a  gas  at 
constant  volume  is  Kv,  and  at  constant  pressure  Kp.  We  may  write 
then  the  two  equations 

KV  =  JCV, (1) 

and 

KP  =  JCP, (2) 

33.  The  Relation  of  the  Specific  Heats  and  the  Density.  Assume  a 
mass  of  gas  weighing  1  pound  to  bo  confined  at  a  temperature  T 
within  a  volume  V\  at  a  pressure  P.  The  volume, 'as  may  be  readily 
seen,  is 

F!  =  -/ (1) 

If  this  mass  of  gas  be  raised  1°  in  temperature  at  constant  pressure, 
its  final  volume  will  become 


ART.  34  THE   RATIO  OF   THE   SPECIFIC   HEATS  21 

The  change  in  volume  will  be 

v       v       R(T  +  V      RT 

ri  -  v\  =     — p—       -p-,    ; (3) 

and  therefore,  after  multiplying  by  P  we  have, 


Now  the  first  term  of  the  equation  is  the  work  done  by  the  pound 
of  gas  in  expanding  at  constant  pressure  while  the  gas  is  rising  1°  in 
temperature,  which,  as  we  have  just  seen,  is  equal  to  the  difference  in  the 
two  dynamic  specific  heats  of  the  gas.  Hence  we  may  write 

R  =  Kp  -  Kv  =  J  (Cp  -  Cv),    ......     (5) 

34.  The  Ratio  of  the  Specific  Heats.  The  ratio  of  the  specific  heat 
of  a  gas  at  constant  pressure  to  its  specific  heat  at  constant  volume  is 
a  function  very  much  used  in  thermodynamic  work,  and  is  designated 
by  the  Greek  letter  f.  Its  value  may  be  expressed  mathematically  by 
the  equation 


The  values  of  7-  and  of  Cv  (and  therefore  of  Kv)  are  difficult  of  direct 
determination.  The  values  of  R  and  Cp  (and  therefore  of  Kp)  are 
easy  of  direct  determination.  Therefore,  the  values  of  7-  and  Cv  are 
best  determined  by  computation  from  the  values  of  Cp  and  R,  quantities 
which  may  be  obtained  with  great  accuracy  from  density  determination 
and  calorimetry  measurements.  It  has  already  been  shown  that 

R  =  Kp  -  Kv,     ........     (2) 

Hence  Kv=  Kp-  R,  .........     (3) 

and  r-K^g  ...........  (-» 

The  values  of  j-  and  Cv  given  in  the  table  on  page  23  were    computed 
from  the  above  equations. 

It  will  be  apparent  from  the  relations  just  shown  that  the  two 
specific  heats  and^fie  function  f  of  a  perfect  gas  are  constant  quantities. 
In  the  case  of  an  imperfect  gas,  however,  it  will  be  seen  that  since  R 
is  not  the  same  under  all  conditions,  the  values  of  one  or  both  of  the 


22  THE  THERMAL   PROPERTIES  OF  GASES  ART.  ^ 

specific   heats,   and   of  the   function   7-,   will   vary   as  the   conditions  o 
temperature  and  pressure  are  changed.  ^ 

35.  The  Intrinsic  Energy  of  a  Gas.  When  a  gas  is  heated  at  constant 
volume  the  amount  of  heat  transferred  to  it  is  utilized  entirely  in 
raising  the  temperature  of  the  gas,  and  therefore  in  increasing  the 
quantity  of  energy  which  the  gas  possesses.  The  energy  so  added  is 
called  intrinsic  energy,  since  it  resides  within  the  gas,  and  is  not  trans- 
ferred by  the  gas  to  any  other  body. 

When  a  gas  is  heated  at  constant  pressure,  we  have  seen  that  soro 
of  the  energy  imparted  to  it  is  expended  in  doing  external  work,  i.e. 
in  pushing  back  the  confining  walls.  The  intrinsic  energy  contained 
in  the  gas  after  a  given  rise  in  temperature  is  the  same  whether  the  gas 
be  heated  at  constant  volume  or  constant  pressure,  but  the  heat  required 
in  the  latter  case  is  greater  than  the  intrinsic  energy  imparted  to  the 
gas  by  the  amount  of  external  work  done.  It  will  be  seen  then  that 
the  intrinsic  energy  of  1  pound '  of  a  perfect  gas  1  is  equal  to  the 
dynamic  specific  heat  of  the  gas  at  constant  volume,  multiplied  by  the 
absolute  temperature  of  the  gas.  Also  if  the  external  work  performed 
by  1  pound  of  such  a  gas,  while  expanding  at  constant  pressure  from 
a  temperature  of  absolute  zero,  be  added  to  its  intrinsic  energy,  their 
sum  will  equal  the  product  of  the  dynamic  specific  heat  at  constant 
pressure  into  the  absolute  temperature  of  the  gas. 

36.  The  Joule-Thompson  Effect.  It  follows  from  the  above  discussion  of  intrinsic 
energy  that  when  a  perfect  gas  expands  without  performing  external  work  that  its 
temperature  will  remain  unchanged,  since  its  intrinsic  energy  remains  unchanged. 
This  statement  is  known  as  Joule's  law.  The  truth  of  this  law  may  be  tested  by 
allowing  a  gas  to  flow  from  a  region  of  high  pressure  to  a  region  of  low  pressure 
through  a  porous  plug  of  very  considerable  thickness,  as  for  instance,  a  small  tube 
tightly  packed  with  cotton  for  a  length  of  6  inches  or  more.  It  has  been  found  that 
under  such  circumstances  the  difference  in  temperature  of  the  gas  before  and  after 
expanding  is  very  small.  In  the  case  of  some  gases,  such  as  hydrogen,  nitrogen,  and 
the  monatomic  gases,  it  amounts,  at  the  most,  to  a  few  hundredths  of  a  degree  per 
atmosphere  difference  in  pressure.  Were  the  gases  perfect,  there  would  be  absolutely 
no  change  in  temperature.  The  amount  of  deviation  from  Joule's  law  marks  the 
degree  of  imperfection  of  the  gas.  A  careful  study  of  the  properties  of  gases,  con- 
ducted by  many  men  and  extended  over  many  years,  shows  that  so  far  as  engineering 
calculations  are  concerned,  that  oxygen,  hydrogen,  nitrogen,  and  the  monatomic 
gases  and  mixtures  of  these  gases  are  sensibly  perfect  at  ordinary  temperatures. 

In  further  proof  of  this  fact  we  may  note  that  the  differences  in  the  temperatures 
indicated  by  thermometers  using  these  different  gases  under  identical  conditions 
are  at  the  most  only  about  yioo  part  of  a  degree  Fahrenheit,  between  the  ice-point 
and  the  boiling-point,  and  are  less  than  yio  of  a  degree  (i.e.,  about  V100  of  one  per 
cent)  at  the  extreme  temperatures  for  which  such  instruments  are  usually  used. 
However,  gases  which  are  sensibly  perfect  at  ordinary  temperatures  are  not  neces- 

1  I.e.,  one  that  is  perfect  at  all  temperatures.  •». 


HOBS.  1-8 


TABLE  OF  THE  PROPERTIES  OF  GASES 


23 


irily  even  approximately  perfect  at  very  low  or  very  high  temperatures,  although 
icy  are  assumed  to  be  so,  for  purposes  of  convenience,  in  many  engineering 
alculations. 

The  characteristic  equations  for  imperfect  gases  and  an  account  of  the  probable 
causes  of  such  imperfections  will  be  found  in  Chapter  XXVI. 

TABLE  VIII 
THERMAL   PROPERTIES   OF   GASES 


Name  of  Gas. 

Chemical 
Symbol. 

Density.* 

R 

r 

cp 

cv 

Air              

0.080710 

53  .  338 

1.4068 

0  .  23727 

0.16867 

Acetylene  

C2H2 

0.07251 

59.37 

Argon         

A 

0.11126 

38.70 

1  .  6667 

0.24890 

0  .  14934 

Carbon  dioxide  f  
Carbon  monoxide  
Ethylene  f  

CO2 
CO 
C2H4 

0.12262 
0.07807 
0.07809 

35.11 
55.14 
55.13 

1.315 
1.415 
1.213 

0.1886 
0.2425 
0.4040 

0  .  1434 
0.1716 
0.3331 

Helium                       .    .    . 

He 

0.01189 

362.0 

1.6667 

2  .  3280 

1  .  3968 

Hydrogen  
Marsh-gas 

H2 
CH, 

0.005588 
0.04464 

770.4 
96.44. 

1.4102 
1.2646 

3.40559 
0  .  59295 

2.41474 
0.46892 

Nirtic  oxide          

NO 

0.0838 

51.37 

1.3994 

0.23150 

0.16543 

Ntirogen  
Oxygen              . 

N2 
O2 

0.07831 
0.08921 

55.10 
48.256 

1.4099 
1.3997 

0.24356 
0.21729 

0.17268 
0.15523 

Steam  f 

H,O 

85.72 

1.285 

0.4614 

0.3512 

Sulphurous  anhydride  f  . 

' 

S02 

0.1793 

24.09 

1.251 

0.1544 

0.1234 

*  Lbs.  per  cu.ft.  at  32°  F.  and  1  atmosphere. 

t  The  properties  of  these  gases  vary  greatly  with  the  temperature  and  pressure. 

PROBLEMS 

1.  A  quantity  of  air  is  confined  within  a  volume  of  2  cu.ft.,  at  a  pressure  of  3000  Ibs. 
per  square  foot.     What  will  be  its  volume  at  the  same  temperature,  if  its  pressure 
is  reduced  to  1000  Ibs.  per  square  foot?  Ans.     6  cu.ft. 

2.  What  will  be  the  pressure  of  the  above  mass  of  air,  if  its  volume  is  made  4  cu.ft.? 

Ans.     1500  Ibs.  per  square  foot. 

3.  A  certain  substance  has  a  temperature  of  50°  F.     What  is  its  absolute  tem- 
perature in  Fahrenheit  degrees?  Ans.     509.6°. 

4.  A  certain  substance  has  an  absolute  temperature  of  660°.     What  is  its  Fah- 
renheit temperature?  Ans.     199.4°. 

6.  A  certain  substance  has  a  temperature  of  104°  F.     What  is  its  absolute  tem- 
perature in  Centigrade  degrees?  Ans.     313.1°. 

6.  A  gas  is  confined  within  a  given  volume  at  a  temperature  of  1000°  absolute 
and  has  a  pressure  of  1000  Ibs.  per  square  foot.     What  will  be  its  pressure  if  its 
temperature  is  raised  to  1500°  absolute  without  changing  its  volume? 

Ans.     1500  Ibs.  per  square  foot. 

7.  A  quantity  of  gas  having  a  temperature  of  600°  Absolute  is  heated  until  its 
pressure  is  doubled,  without  change  in  volume.     What  is  its  final  temperature? 

Ans.     1200°  absolute,  or  740.4°  F. 

8.  A  quantity  of   gas   having  a  pressure  of  2500  Ibs.  per  square  foot  and  a  tem- 
perature of  60°  F.  is  raised  in  temperature  to  250°  F.  without  change  in  volume. 
Find  its  final  pressure.  Ans.     3414  Ibs.  per  square  foot. 


24  THE  THERMAL  PROPERTIES  OF  GASES  PROBS.  9-23 

9.  A  quantity  of  gas  having  an  initial  pressure  of  50  Ibs.  per  square  inch  absolute, 
and  temperature   of  60°  F.   is  raised  to  a  pressure  of  80  Ibs.   per  square  inch  by 
heating  without  change  in  volume.     Find  the  final  temperature.         Ans.     371.8°  F. 

10.  What  will  be  the  value  of  the  constant  R  for  chlorine  gas,  chlorine  gas  being 
diatomic  and  the  atomic  weight  of  chlorine  being  35.5?  Ans.     /2  =  21.75. 

11.  A  certain  mixture  of  gases  has  a  density  of  0.88  as  compared  with  air;    what 
will  be  the  value  of  the  constant  R  for  this  mixture?  Ans.     72=60.61 

12.  How  many  pounds  of  the  above  mixture  will  be  contained  in  a  cylindrical 
gasometer  50  ft.  in  diameter  and  40  ft.  high,  at  atmospheric  pressure  and  a  tem- 
perature of  80°  F.?  Ans.     5088  Ibs. 

13.  What  volume  will  1  Ib.  of  marsh-gas  (CH4)  occupy  at  a  temperature  of  100°  F. 
and  a  pressure  of  10,000  Ibs.  per  square  foot?  Ans.     5.40  cu.ft. 

14.  A  tank  contains  2  Ibs.  of  oxygen  at  a  pressure  of  400  Ibs.  per  square  inch 
absolute  and  a  temperature  of  60°  F.     What  is  its  volume?  Ans.     0.8707  cu.ft. 

15.  A   cylindrical   tank   6   ins.    in   diameter   and    3    ft.    long  contains   1^  Ibs.  of 
acetylene,    whose    formula   is    C2H2.     At    what  temperature  will  the  pressure  within 
this  cylinder  reach  500  Ibs.  per  square  inch  gage?  Ans.     129.2°  F. 

16.  A  quantity  of  gas  has  a  pressure  of  800  mm.  of  mercury,  a  volume  of  1  liter, 
and   its   temperature   is    15°  C.     What   will   be   its   temperature   when  the   pressure 
becomes  1000  mm.  of  mercury  and  the  volume  1.1  liters?  Ans.     123°  C. 

17.  The  specific  heat  of  a  £as  at  constant  pressure  is  3.000.     The  value  of  R  for 
this  gas  is  700.     Find  the  value  of  its  specific  heat  at  constant  volume. 

Ans.     Cv  =  2.101. 
.    18.  Find  the  value  of  the  constant  7-  for  the  above  gas.  Ans.     7- =  1.428. 

19.  Assuming  that  7-  for  air  equals  1.406,  compute  from  the  value  of  R  given  in 
Art.  30,  the  value  of  the  dynamic  specific  heat  of  air  at  constant  volume. 

Ans.     Kv  =  131.4  ft  .-Ibs. 

20.  Compute  the  specific  heat  of  air  at  constant  pressure.  Ans.     Cp=  0.2375. 

21.  What  quantity  of  heat  will  be  required  to  raise  the  temperature  of  2  Ibs.  of 
air  confined  at  constant  pressure,  from  40°  to  90°  F?  Ans.     23.75  B.T.U. 

22.  What  will  be  the  increase  in  the  intrinsic  energy  of  the  air  in  the  above  case? 

Ans.     16.89  B.T.U. 

23.  What  will  be  the  external  work  performed  in  the  above  case? 

Ans.     5334  ft.-lbs. 

(Note  the  relation  between  the  intrinsic  energy,  the  external  work,  and  the  heat 
imparted.) 


CHAPTER  III 
THE  EXPANSION   OF   GASES 

37.  The    Pressure    Volume    Diagram.     The     relation   between    the 
pressure  and  volume  of  a  mass  of  homogeneous  fluid  expanding  by  any 
definite  law  may  be  expressed  by  means  of  an  equation  involving  these 
two  quantities  only  as  variables.     The  locus  of  the  simultaneous  values 
of  the  pressure  and  volume  of  an  expanding  fluid,  when  plotted  as  a 
curve  whose  ordinates  are  pressures  and  whose  abscissae  are  volumes, 
is  known  as  the  pressure  volume  or  PV  curve  of  the  expanding  fluid. 
The  equation  of  this  curve  is  obviously  the  equation  relating  the  pressure 
and  the  volume  of  the  expanding  fluid.     If  a  series  of  such  curves  is 
collected  on  one  diagram,   in  order  to  show  graphically  the  changing 
states  of  a  mass  of  fluid,  the  diagram  is  termed  a  Watt  diagram,  and 
is  also  known  as  a  PV  diagram  or  an  indicator  card.     Since  areas  on 
such  diagrams  represent  the  product  of  pressure  and  volume,  they  also 
represent  work  or  energy.     The  use  of  such  curves  and  diagrams  is  not 
only  convenient,  but  necessary,  in  illustrating  the  principles  of  thermo- 
dynamics, and  in  investigating  the  performance  of  most  thermodynamic 
machinery. 

38.  The  Four  Cases  of  Expansion.     When  a  gas  is  allowed  to  expand 
there  are  four  definite  conditions  under  which  the  expansion  may  take 
place.     In  the  first  case  the  gas  expands  at  constant  temperature,  and 
since  it  does  work  by  its  expansion,  this  necessitates  the  addition  of 
heat  to  the  gas  in  order  to  maintain  its  temperature  at  a  constant  value. 
This    is    termed    isothermal    expansion.     In    the    second    case    the     gas 
expands   without  the   addition  or  abstraction   of  heat.     Since  the  gas 
does  work  by  its  expansion,  some  of  the  energy  contained  in  the  gas 
as  heat  is  lost,  or  rather  transformed,   in    order  to  perform  this  work. 
This  is  termed  adiabatic  expansion.      In  the  third  place,  the  gas  expands 
without  undergoing  a  change  of  pressure.     Since  it  does  work  by  its 
expansion,  and  the  product  of  its  pressure  and  volume   (and  therefore 
its  temperature)   increases,  heat  must  be  added  both  to  do  the  work 
and  to  raise  its  temperature.     This  is  termed  isobaric  expansion.     In 
the   fourth   case  the   loss  in  intrinsic   energy   of  the   expanding  gas   is 
proportional  to  the  external  work  of  expansion.     This  is  termed  poly- 
tropic  expansion. 

25 


26 


THE  EXPANSION  OF  GASES 


ART.  39 


39.  Isothermal  Expansion.  During  the  isothermal  expansion  of  a 
sensibly  perfect  gas  the  mass  of  gas  being  at  a  constant  temperature, 
its  pressure  and  volume  must  be  such  that  PV=WRT,  where  W,  R, 
and  T  are  all  constants.  Therefore,  the  relation  between  the  pressure 
and  volume  at  any  instant  during  isothermal  expansion,  may  be  expressed 
by  the  equation 

PV  =  C  -  PiFi, 

where  P  and  V  are  both  variables,  and  C  is  a  constant  equal  to  the 
product  of  the  initial  pressure  and  volume.  This  is  the  equation  of  a 
second  degree  curve,  which  is  known  in  analytic  geometry  as  the  equi- 


FIG.  4. — The  isothermal  expansion  line. 

lateral  hyperbola,  the  form  of  which  is  shown  in  Fig.  4.  The  curve 
is  asymptotic  to  both  its  axes. 

40.  Graphical    Construction    of    the    Equilateral    Hyperbola.     The 

isothermal  expansion  line  may  be  constructed  by  the  method  shown 
in  Fig.  5.  Let  A  be  any  point  on  the  curve  for  which  the  pressure  and 
corresponding  volume  are  known.  Through  A  draw  vertical  and 
horizontal  lines  marked  VV  and  HH  respectively,  in  the  figure.  From 
0,  the  origin  of  axes,  draw  lines  OB,  OC,  OD,  etc.  Through  the  inter- 
sections of  these  lines  with  VV  draw  horizontals  as  GJ,  and  through 
their  intersections  with  HH  erect  perpendiculars  as  IJ.  The  inter- 
sections of  these  perpendiculars  with  the  corresponding  horizontals  are 
points  on  the  equilateral  hyperbola  passing  through  A  and  asymptotic 
to  the  axes.  Conversely,  if  through  two  points  on  such  an  expansion 
line  perpendiculars  and  horizontals  are  drawn,  and  a  diagonal  is  drawn 


ART.  40         WORK   DONE   DURING   ISOTHERMAL  EXPANSION 


27 


through  the  rectangle  so  formed,  the  diagonal  produced  will  pass  through 
the  origin  of  axes. 


FIG.  5. — Graphical  construction  of  the  equilateral  hyperbola. 

41.  Work  Done  During  Isothermal  Expansion.  In  order  to  find  the 
work  done  by  a  mass  of  gas  expanding  isothermally,  we  must  multiply 
the  change  in  volume  by  the  mean  pressure  during  the  expansion.  Let 
us  suppose  that  the  gas  expands  from  the  condition  P\V\,  to  the  con- 
dition P2^2.  The  change  in  volume  will,  of  course,  be  V2—V\.  The 
mean  pressure  during  expansion  is  the  mean  ordinate  included  under 
the  pressure  volume-curve  between  the  pressures  PI  and  P^-  The  mean 
ordinate  multiplied  by  the  change  in  volume  must,  of  course,  be  equal 
to  the  work  done,  and  therefore  to  the  shaded  area  included  under  the 
curve  in  Fig.  4. 

Since  the  temperature  remains  constant  during  the  expansion,  we 
have  for  the  value  of  PV  at  any  point  during  the  expansion, 


p  V  =  C  =  PiV} 


from  whence 


C 
V 


Now,  since  the  work  done  during  any  small  expansion  is  given  by 
the  equation 

dU  =  P  dV,    .........     (1) 

the  work  done  during  any  isothermal  expansion  may  be  expressed  by 
the  equation, 


v*  r 
,   VdV 


Integrating,  we  have 


0) 


28  THE   EXPANSION   OF   GASES  AKT.  42 

Now,  since  the  product  of  the  pressure  and  volume  are  always  equal 
to  C,  the  product  of  the  initial  pressure  and  the  initial  volume  will,  of 
course,  be  equal  to  C,  and  we  may  substitute  P\V\  for  (7.  The  ratio 
of  the  final  to  the  initial  volume  is  known  as  the  ratio  of  expansion  and 
usually  denoted  by  the  symbol  r.  We  may  therefore  write  the  above 
equation  in  the  form 

U=P1V1loger (4) 

This  may  also  be  written  in  the  form 

U  =  W  R  T  loge  r (5) 

In  the  above  equations 

£7  =  the  work  done,  in  foot-pounds,  by  a  mass  of  gas  expanding  iso- 

thermally; 
W  =  the  mass  of  the  gas  in  pounds ; 

T  =  the  absolute  temperature  of  the  gas ; 
PI  =  the  initial  pressure  in  pounds  per  square  foot, 
FI  =  the  initial  volume  in  cubic  feet ;  and 

r  =  the  final  divided  by  the  initial  volume. 

It  will  be  noted  that  as  the  gas  continues  to  expand  to  a  larger  and 
larger  volume,  the  ratio  of  expansion  will  increase  indefinitely  with 
the  volume.  Hence  the  work  done  by  a  mass  of  gas  expanding  iso- 
thermally  to  an  infinite  volume  is  infinite  in  amount.  Since  the  tem- 
perature of  the  gas  remains  constant,  the  intrinsic  energy  of  the  gas 
will  also  remain  constant  and  the  heat  added  to  effect  isothermal 
expansion  is  entirely  transformed  into  work.  Were  it  possible  to  devise 
an  apparatus  which  could  make  use  of  the  infinite  isothermal  expansion 
of  a  gas,  we  would  have  a  heat  engine  capable  of  transforming  the  entire 
quantity  of  heat  energy  transferred  to  it,  into  work.  However,  it  is, 
so  far  as  we  know,  not  possible  to  construct  such  an  engine. 

42.  Relation  between  the  Changes  in  Pressure,  Volume,  and  Tem- 
perature of  an  Expanding  Gas.  Assume  that  1  pound  of  a  sensibly 
perfect  gas  expands  by  any  law  whatever,  and  thereby  undergoes 
simultaneously  a  change  of  temperature,  pressure,  and  volume.  Let 
the  initial  temperature  of  the  gas  be  T,  the  initial  pressure  P,  and  the 
initial  volume  V.  Let  us  assume  that  the  change  of  temperature  result- 
ing from  the  expansion  is  dT,  the  change  of  pressure  is  dP  and  the 
change  of  volume  is  dV.  In  case  the  pressure,  temperature,  or  volume 
are  increased,  the  respective  changes  will  be  positive,  and  in  case  they 
are  decreased,  they  will  be  negative.  Then,  after  expansion,  we  will 
have  for  the  final  volume  V +dV,  for  the  final  pressure  P  +  dP,  and  for 


ART.  43  ADIABATIC  EXPANSION  29 

the  final  temperature  T  +  dT,  where  dP  and  dT  may  be  either  positive 
or  negative.  From  the  characteristic  equation  of  gases  we  have  PV  =  RT 
for  1  pound  of  any  gas,  and  therefore  after  the  expansion 


(1) 

Multiplying  this  out,  we  will  have 

i 

PV  +  PdV  +  VdP  +  dPdV  =  RT+RdT  .....     (2) 
Since  PV  =  RT  and  in  the  limit  dP  dV  vanishes,  we  may  write 

P'dV+VdP=*RdT       .......     (3) 


or 


which  is  an  equation  relating  the  change  in  temperature  of  an  expanding 
gas  to  the  changes  in  pressure  and  volume.  If  the  temperature  falls, 
dT  will  be  negative,  and  since  in  most  cases  of  expansion  the  pressure 
also  falls,  dP  is  also  usually  negative. 

43.  Adiabatic  Expansion.  When  a  gas  expands  adiabatically,  it 
loses  heat,  since  a  part  of  its  intrinsic  energy  is  transformed  into  the 
mechanical  work  of  expansion.  If  the  expansion  be  infinitesimal,  the 
work  done  is  expressed  by  the  equation 

dU=PdV,     .........     (1) 


in  which  dU  is  the  quantity  of  work  performed  by  the  gas,  P  is  the 
pressure  and  dV  is  its  change  in  volume.  The  loss  of  intrinsic  energy  is 
equal  to  the  specific  heat  of  the  gas  at  constant  volume,  Kv,  multiplied 
by  the  change  in  temperature,  dT.  Since  the  temperature  falls,  dT  is 
negative,  and  therefore  the  heat  lost  by  the  gas  is  expressed  by  the 
equation 

dH=~KvdT  ..........     (2) 

Since  the  loss  of  intrinsic  energy  is  equal  to  the  work  of  expansion, 
we  may  write 

PdV=~KvdT  ..........     (3) 

We  have  shown  in  the  preceding  paragraph  that 


JK 


30  THE  EXPANSION   OF   GASES  ART.  43 

Substituting  (4)  in  (3),  we  have 


......     (5) 

J.V 

Since 

T£ 

Kv  =  KP-R,      and      jf  -  r, 

J\v 

we  have 


ft  r       1" 

Xl/  7^  —  1 

Substituting  (6)  in  (5)  we  have 

PdV=  -~~I(VdP  +  PdV)> (7) 

which  becomes 

rPdV  =   -VdP (8) 

Dividing  through  by  PF  we  have 

dV       _dP 
J  V         ~  P' 

Integrating  each  side  between  corresponding  limits 

-  -£-? °» 

which  becomes 

f  (loge    V-loge  Vi)    =  loge  PI -loge  P,        ....       (11) 

or 

rloge^   =log.^^ (12) 

whence 

and 

PF^PiF/ (14) 

In  the  above  equation,  P  is  the  pressure  and  F  is  the  corresponding 
volume  of  a  quantity  of  sensibly  perfect  gas  undergoing  adiabatic 
expansion  (or  compression)  when  the  original  pressure  of  the  gas  was 
PI  and  its  original  volume  V\.  This  expression  may  also  be  written 

PVr=C, (15) 

in  which  C  is  a  constant. 


ART.  44    RELATION   BETWEEN   INITIAL  AND   FINAL   PRESSURE  31 

44.  Relation  between  Initial  and  Final  Pressure,  Volume,  and  Tem- 
perature of  a  Gas  Expanding  Adiabatically.  If  the  gas  be  assumed  to 
have  expanded  to  some  pressure  P2,  and  corresponding  volume  V2  we 
will  of  course  have  the  relation 


-PiVir .     (1) 

This  may  be  written 

7l/-£.  ........  (2) 

For   the   characteristic   equation   of  gases,  we  have  for  1  pound  of  any 
gas 

T=   ~R~' 

and  therefore 


P\v 

p 

For  -^  in  (3)   we  may  substitute  its  value  from  equation   (2),  and 
obtain  the  relation 


'i     (Y*\r~l 
^(vl)       ' 

From  number  (2)  we  may  write 

F2=/Pi\7 
F!     \P2] 


y 
Substituting  this  value  for  •==-  in  equation  (3)  we  have 


r-l 


Solving  equations  (2)  and  (4)  for  F2,  (1)  and  (6)  for  P2,  and  (4)  and 
(6)  for  T2  we  will  have 


c.  P,-,,'. 


32  THE  EXPANSION   OF  GASES  ART.  45 

These  equations  may  be  readily  solved  by  the  use  of  a  table  of 
logarithms  when  they  are  written  in  the  form 

A',  log  ^logF^  -  lo 

T 


B'.  log  K2  =  log  Vi+j= 
C'.  logP2  =  logP1+  r'lo 
D'.  log  P2  =  log  Pl+  ^ 
E'.  log  T2  =  log  TVKr-l)  log 
F.  Io7^  =  lo7\+ 


By  means  of  these  relations  we  may  compute  the  final  temperature, 
pressure,  or  volume  of  a  mass  of  gas  expanding  adiabatically,.  when  its 
initial  temperature,  pressure  or  volume  is  known,  and  also  the  ratio  of 
its  initial  and  final  pressure,  temperature,  or  volume.  It  is  to  be  noted 
that  these  equations  will  be  true,  no  matter  what  system  of  units  be 
employed.  For  instance,  the  temperatures  may  be  expressed  in  Centi- 
grade or  Fahrenheit  degrees  on  the  absolute  scale,  the  pressure  in  pounds 
per  square  inch  or  per  square  foot,  or  in  atmospheres,  or  in  inches  or 
millimeters  of  mercury,  and  the  volumes  in  per  cent,  in  cubic  feet,  in 
cubic  inches,  or  in  cubic  centimeters  or  liters.  So  long  as  the  same 
system  of  units  is  employed  throughout  an  equation,  the  results  obtained 
will  be  correct. 

45.  Work  Done  During  Adiabatic  Expansion.  The  amount  of  work 
done  by  a  mass  of  gas  expanding  adiabatically  will  of  course  be  equal 
to  the  heat  lost  by  the  gas.  Therefore  we  may  write 

U=  W  KV(T,-T2)  ........     (1) 

Substituting  for  TI  the  value  *  *  and  for  T2  the  value  -^~jj,  we 
may  write  this  expression, 

TT        W 

u  'W 


ART.  46  WORK   OF  ADIABATIC   EXPANSION  33 

Clearing  this,  we  will  have 


P2V2) .     .     (3) 

JUi 

From  equation  (6),  Art.  43,  we  have  the  relation 

S-Fi (4) 

Substituting  this  we  will  have 


«•> 


in  which  C7=the  number  of  foot-pounds  of  work  done  by  a  mass  of  gas 

expanding  adiabatically; 

PI  =  the  initial  pressure  of  the  gas  in  pounds  per  square  foot ; 
P2  =  the  final  pressure  in  the  same  units; 
Fi  =  the  initial  volume  of  the  gas  in  cubic  feet; 
F2  =  the  final  volume  in  the  same  units. 

This  same  result  may  be  obtained  by  the  integration  of  the  expression 

U=CV*PdV, (6) 

•sVl 

in  which  we  substitute  for  P   the   value   obtained  from  equation    (C), 

Art.  44,  namely, 

(y 
v 

The  integral  of  this  expression  is,  of  course,  equal  to  the  shaded  area  in 
Fig.  6,  which  shows  the  pressure-volume  curve  of  a  mass  of  gas  expand- 
ing adiabatically.  This  curve  is  also,  like  the  rectangular  hyperbola, 
asymptotic  to  both  axes,  but  it  will  be  noted  that  the  area  included 
under  this  curve  from  the  volume  V\  to  an  infinite  volume  is  not  infinite 
in  amount,  but  is  a  definite  and  finite  quantity,  as  will  be  seen  from 
equation  (1)  in  this  article.  By  such  an  expansion  the  gas  will 
part  with  the  entire  amount  of  intrinsic  energy  which  it  contains,  and 
the  work  of  expansion  is  limited  to  this  quantity  of  energy. 

46.  Graphical  Construction  of  the  Curve  whose  Equation  is  PVn  =C. 
Any  curve  represented  by  the  general  equation 

PVn  =  C 


34 


THE  EXPANSION  OF  GASES 


ART.  46 


may  be  constructed  graphically  by  the  method  shown  in  Fig.  7,  when 
one  point  on  the  curve,  and  the  value  of  the  index  n  are  known.  Let 
the  coordinates  of  point  M  be  PI  and  V\,  and  the  coordinate  axes  be 


FIG.  6. — The  adiabatic  expansion  line. 


FIG.  7. — Graphical  construction  of  the  curve  P  Vn  =  K. 

OP  and  0V.     Draw  AO,  making  any  convenient  angle  AO V  with  OF. 
Then  let 


ART.  47  ISOBARIC  EXPANSION  35 

Determine  the  angle  BOP,  whose  tangent  is  given  by  the  equation, 

tan  BOP  =  —  ^, 
JL 

and  construct  angle  BOP.  Through  M  draw  the  horizontal  line  Me  and  the 
vertical  line  Md,  intersecting  OB  at  c  and  Oa  at  d  respectively.  Through 
c  and  d  draw  ce  and  df,  making  angles  of  45°  with  the  coordinate  axes, 
and  intersecting  them  at  e  and  /.  Through  e  draw  a  horizontal  .and 
through  /  a  perpendicular,  intersecting  at  N,  which  will  be  a  second  point 
on  the  curve.  In  like  manner  points  I  and  q  and  as  many  more  points 
as  are  desired,  may  be  located. 

An  inspection  of  the  figure  will  show  that  if  Pl  and  Vl  be  the  coordinates  of  M, 
and  P  and  V  those  of  N,  that 


......     (1) 

and 


(2) 
From  equation  (2)  we  may  write 

Vn=Vln(l+tB.nAOV)«  .........     ....     (3) 

Hence 

PV*  =  P1F1n  =  P1tYl(l-tan50P)(l;ftaiiAOF)n  .....     (4) 

Dividing  both  sides  by  P^V^  we  have 

(l-tanBOP)(l+tanAOF)»=l  ........     (5) 

From  which  we  deduce  that 

.     .     (6) 


Clearing  (6), 

X-Xt&nBOP=l  ..........     (7) 

Solving  for  tan  BOP, 


.      .  (8) 

JL 

Hence  a  curve  constructed  in  the  manner  described  will  satisfy  the  equation 

P  vn  =  PlVln  =  C. 

It  will  often  be  more  convenient  to  determine  the  angles  AOV  and  BOP  by 
computing  the  coordinates  of  a  second  point  upon  the  curve,  such  as  N,  and  then 
after  drawing  Ne  and  Nf,  ec,  and  fd,  and  Me  and  Md,  finally  draw  OB  and  OA 
through  the  intersections  of  ec  with  Me,  and  fd  with  Md,  respectively. 

47.  Isobaric  Expansion.  The  equation  for  isobaric  expansion  is 
P  =  k,  a  constant,  since  the  pressure  remains  constant.  The  PF  curve 
is  therefore  a  horizontal  line. 

During  isobaric  expansion,  the  quantity  of  heat  added  to  the  gas 
is  of  course 


36  THE  EXPANSION  OF   GASES 

The  work  done  during  isobaric  expansion  is  equal  to 


ART.  47 


The  amount  of  intrinsic  energy  imparted  to  the  gas  is  equal  to 

W  KV(T2-  Ti). 

f 

We  may  also  express  the  amount  of  work  done  during   the  isobaric 
expansion  in  terms  of  the  temperatures  by  the  expression 

W 


FIG.  8. — Work  of  isobaric  expansion  and  increase  in  intrinsic  energy. 

We  may  express  the  quantity  of   heat  imparted  to  the  gas  in  terms 
of  the  pressure  and  volumes,  by  the  expression 


/ 

If  an  adiabatic  be  drawn  from  the  state  P\Vi  and  another  to  be 
drawn  from  the  state  P^V^  of  a,  gas  undergoing  isobaric  expansion,  as 
in  Fig.  8,  the  intrinsic  energy  of  the  gas  at  the  beginning  of  expansion 
will  be  represented  by  the  area  under  the  first  adiabatic,  the  intrinsic 
energy  at  the  end  of  the  expansion  will  be  represented  by  the  area  under 
the  second  adiabatic,  and  the  energy  imparted  to  the  gas  will  be  repre- 
sented by  the  difference  between  these  areas  plus  the  work  of  expansion 
which  is  represented  by  the  area  under  the  isobaric  line.  This  is, 
obviously,  the  shaded  area  plus  twice  the  blackened  area. 


ART.  48  POLYTROPIC  EXPANSION  37 

48.  Polytropic  Expansion.  The  work  performed  by  a  mass  of  gas 
undergoing  polytropic  expansion  is  equal  to  a  constant  times  the  loss 
in  intrinsic  energy.  Hence  we  may  write 

PdV=-aKvdT,  ........     (1) 

by  analogy  with  equation  (3),  Art.  43.  Making  the  same  substitutions 
as  were  made  in  the  former  equation  and  transposing  the  constant  a  to 
the  left-hand  member  we  will  obtain 


'  ......  •  •  • 

which  is  similar  in  form  to  equation  (9)  of  that  article.  Substituting  n 
for  —  —  ,  we  will  finally  obtain  the  relation, 

PVn  =  P1V1n  =  C,   ........     (3) 

which  is  similar  in  form  to  equation  (14)  of  Art.  43,  and  is  the  equation 
giving  the  relation  between  the  pressure  and  volume  of  a  mass  of  gas 
undergoing  polytropic  expansion. 

49.  The  Relation  between  the  Initial  and  Final  Pressure,  Volume, 
and  Temperature  of  a  Gas  Undergoing  Polytropic  Expansion.     From 
equation    (e)    in   the   preceding   paragraph,    the    relations   between   the 
initial  and  final  pressure  temperature  and  volume  of  a  mass  of  gas  under- 
going polytropic  expansion  may  be  deduced  by  the  methods  outlined 
in  Art.  44.     By  substituting  n  for  7-  in  the  equations  A  to  F  and  A'  to 
F'  in  that  article,  the  relation  between  the  initial  and  final  pressure, 
temperature,    and   volume   of   a   gas   undergoing   polytropic   expansion, 
may  be  computed.     In  the  same  way  by  substituting  aKv  for  Kv  and 
n  for  7-  in  the  equations  in  Art.  45,  the  work  done  during  polytropic 
expansion  may  be  computed.     In  case  the  value  of  the  exponent  n  is 
very  nearly  unity,  exact  computations  of  the  work  done  during  polytropic 
expansion  are  not  feasible.     In  case  it  is  desirable  to  determine  exactly 
the   work   done    during   such   expansion   the    area   included   under   the 
expansion  line  may  be  measured,  and  the  work  of  expansion  computed 
from  the  measured  area  and  the  known  scales  of  the  diagram. 

50.  Special  Cases  of    Polytropic  Expansion.       It  may  be  noted    that  the 
isothermal,  adiabatic,  and  isobaric  expansion  may  all  be  considered  special  cases  of 
polytropic  expansion.     When  a=  oo  , 


oo 


38  THE  EXPANSION  OF  GASES  ART.  51 

which  is  the  case   of  isothermal  expansion  where  there   is  no  change   in  intrinsic 
energy.     When  a  =  l, 


which  is  the  case  of  adiabatic  expansion,  where  the  change  in  intrinsic  energy  is 
equal  to  the  work  performed.  When  a  =  l  —  j-,  n=0,  which  is  the  case  of  isobaric 
expansion,  where  the  pressure  is  constant.  When  a=0, 

r-i+o 

n=-T-  -fV? 

which  is  the  case  of  change  of  pressure  without  change  of  volume  (i.e.,  change  in 
intrinsic  energy  without  performance  of  work). 

61.  Expansion  in  Conducting  Cylinders.  Gases  do  not  remain  in  thermody- 
namic  equilibrium  while  they  are  being  expanded  or  compressed  in  practical  thermo- 
dynamic  machines,  since  there  will  in  general  be  a  difference  in  temperature  between 
the  expanding  gas  and  the  conducting  walls  of  the  containing  vessel.  As  a  result  the 
temperature  of  the  layers  of  gas  close  to  the  walls  will  be  different  from  that  of  the 
mass  of  the  gas.  It  is  found,  however,  that  under  these  conditions  the  pressure- 
volume  curve  of  expansion  or  compression  is  very  nearly  a  line  of  polytropic  expansion, 
and  the  value  of  the  index  lies  between  1  and  7-.  Such  expansion  or  compression 
may  be  treated  as  though  it  were  polytropic,  the  value  of  the  index  n  in  the  equation 
PVn  =  C  being  determined  from  the  actual  expansion  curve  by  the  equation 

log  - 


in  which  Pl  and  Vl  and  P2  and  V2  are  corresponding  absolute  pressures  and  volumes 
as  derived  from  the  actual  expansion  line  taken  from  an  indicator  card. 

52.  Compression  the  Converse  of  Expansion.    The  process  of  com- 
pression is  the  reverse  of  the  process  of  expansion,  the  volume  of  the 
gas   progressively   diminishing   as   the   process   continues.     In   order   to 
compress  a  gas,   work  must  be  done  upon  it,  which  accounts  for  the 
fact  that  if  proper  substitutions  be  made  in  any  of  the  formulae  for  the 
work  done  by  an  expanding  gas,  we  will,  in  the  case  of  compression,  get 
a  negative  answer.     For  instance,  in  the  case  of  isothermal  expansion, 
the  final  volume  is  less  than  the  initial  volume,  the  ratio  of  the  volumes 
is  less  than  unity  and  the  logarithm  of  the  ratio  is  a  negative  quantity 
(see  Art.  41,  equation  (4)),  indicating  that  the  gas  does  negative  work 
during  compression.     If  proper  substitutions  be  made  in  the  equations 
giving   quantities   of   heat    absorbed   or   rejected   by   gases   undergoing 
compression,  the  answers  will  also  be  negative,  indicating  that  in  the 
case  of  compression,  the  heat  transfer  is  in  the  opposite  direction  to  what 
it  is  in  the  case  of  expansion. 

53.  The  Velocity  of  Sound.     If  the  pressure  of  a  mass  of  gas  be  suddenly 
increased  at  some  point,  the  pressure  of  the  entire  mass  is  not  raised  instantly,  but 


ART.  53  THE  VELOCITY  OP  SOUND  39 

the  increase  of  pressure  travels  from  point  to  point  in  the  gas  with  a  velocity  depend- 
ing on  the  nature  and  temperature  of  the  gas.  Assume  a  column  of  gas  whose 
cross-section  is  1  square  foot  and  whose  length  is  indefinite,  to  be  confined  within 
a  tube,  under  a  pressure  of  P  pounds  per  square  foot  and  at  the  temperature  T.  If  the 
pressure  at  one  end  of  this  tube  be  increased  suddenly  by  applying  the  force  dP  to 
the  piston  shown  in  Fig.  9  for  one  second,  the  increase  in  pressure,  dP,  will  be  trans- 
mitted to  the  right  with  the  velocity  V  feet  per  second,  and  at  the  end  of  one  second 
V  cubic  feet  of  gas  will  be  compressed.  The  mass  of  this  gas  will  be 

P  V 


Since  the  compression  of  the  gas  is  sudden,  the  gas  does  not  have  time  to  part, 
with  its  heat  to  surrounding  objects,  and  the  compression  is  adiabatic,  the  relation 
between  the  pressure  and  volume  being  expressed  by  the  equation 


from  whence 


dP 


Gas  at  pressure  P 
and  temperature  T. 


FIG.  9. 
Differentiating  this  expression  we  have 

rVr-ldV=-CP~2dP,      .........     (4) 


dv-        CdP 


We  may  substitute  for  C  its  value  from  equation  (2)  and  obtain 

*r-?g  .............   (6) 

In  the  above  expression  dV  is  the  change  in  volume  of  the  gas,  dP  is  the  change  in 
pressure,  and  P  and  V  are  the  initial  pressure  and  volume.  It  will  be  noted  that 
if  the  pressure  increases,  the  volume  diminishes,  as  is  indicated  by  the  minus  sign. 
As  a  result  of  the  application  of  the  constant  force  dP  to  the  gas,  the  end  of 
the  column  is  moved,  in  one  second,  a  distance  dV,  and  the  center  of  gravity 

dV 
of  the  column  is  moved  in  the  same  time  a  distance  —  .     The  acceleration  produced 

by  this  constant  force  in  the  column  of  gas  is  twice  the  distance  which  the  gas  was 
moved  in  the  first  second,  or  dV  feet  per  second  per  second.  Now,  from  a  well- 
known  principle  in  dynamics,  namely,  force  =  mass  X  acceleration,  we  have 

dP  =  _  5  dV  .............     (7) 


40  THE  EXPANSION  OF  GASES  ART.  54 

Substituting  from  1  and  6, 


py 

dP 
Solving  for  V  we  will  have 


(9) 


in  which  V  is  the  rate  of  transmission  of  pressure  in  gas  in  feet  per  second,  and  T  is 
the  absolute  temperature  of  the  gas  in  Fahrenheit  degrees. 

64.  Velocity  of  Transmission  of  Explosive  Pressure  in  Confined  Gases. 
The  above  equations  will  be  true  only  when  the  increase  hi  pressure  is  infinitesimal 
as  compared  with  the  actual  pressure  of  the  gas.  This  is  true  in  the  case  of  sound 
waves,  which  are  transmitted  in  the  gas  with  the  velocity  given  by  the  above 
equation.  When,  however,  the  wave  is  caused  by  a  violent  explosion  which  produces 
a  large  increase  in  pressure,  the  velocity  of  transmission  of  the  pressure  is  higher 
than  the  above  equation  would  indicate. 

If  it  be  assumed  that  the  increase  in  pressure  produced  by  the  suddenly  applied 
force  is  large,  the  final  pressure  produced  may  be  represented  by  P2  while  the  initial 
pressure  may  be  represented  by  Pr  The  final  volume  will  be,  from  equation  (/I), 
Art.  44, 


(8) 


The  decrease   of  the   volume   of  the  mass,   and   therefore,   as  has  already  been 
shown,  the  acceleration  of  the  mass,  will  be 


(9) 


We  may  therefore  write,  by  analogy  from  equation  (8)  of  the  previous  article, 


Solving  for  T^  we  will  have 

y=      jgRT(P2-P3 

(11) 


which  is  an  expression  giving  the  velocity  of  transmission  of  pressure  in  a  gas  when 
the  increase  in  pressure  is  great  as  compared  with  the  original  pressure. 

When  a  combustible  mixture  of  gases  is  confined  under  pressure  and  ignited  at 
some  point,  as  is  the  case  in  most  types  of  gas  engines,  the  increase  in  pressure  pro- 
duced by  the  local  explosion  is  transmitted  throughout  the  mass  of  the  gas  in  the 
same  manner  as.  the  pressure  was  transmitted  through  the  column  described  in 
Art.  53.  As  the  pressure  wave  proceeds  through  the  gas,  it  compresses  it 
adiabatically.  If  the  initial  temperature  of  the  gas  is  sufficiently  high,  so  that  the 
adiabatic  compression  heats  the  mixture  to  its  kindling  point,  the  flame  of  com- 
bustion will  proceed  through  the  mass  with  the  velocity  indicated  by  equation  (11) 
of  the  preceding  paragraph.  If,  however,  the  temperature  of  the  gas  is  not  sufficiently 
high  for  this  action  to  take  place,  the  pressure  in  the  gas  will  increase  gradually,  the 
flame  being  propagated  from  point  to  point  by  heat  conduction  and  radiation,  with 


ART.  55 


FLOW  OF   GAS  THROUGH  AN   ORIFICE 


41 


a  velocity  many  hundred  times  lower  than  that  given.  The  phenomena  of  pressure 
transmission  are  of  great  practical  importance  in  the  theory  of  gas  engines  and  gaseous 
explosions. 

65.  Theory  of  the  Flow  of  Gas  through  an  Orifice.  When  a  gas  flows 
through  a  nozzle,  it  will  be  found  that  as  each  particle  of  the  gas  passes  through  it 
will  expand  in  volume  and  increase  in  velocity.  If  the  ratio  of  expansion  in  volume 
as  the  gas  passes  from  one  cross-section  of  the  nozzle  to  another  is  less  than  the 
ratio  of  increase  in  velocity,  it  must  follow  that  the  nozzle  is  less  in  cross-section  at 
the  second  point  than  at  the  first,  the  nozzle  being  convergent  between  the  two 
sections.  If,  on  the  other  hand,  the  ratio  of  expansion  is  greater  than  the  ratio  of 
increase  in  velocity,  the  cross-section  of  the  nozzle  will  be  greater  at  the  second  point 
than  at  the  first,  the  nozzle  being  divergent  between  the  two  sections. 

In  passing  through  a  nozzle,  a  gas  will  of  course  neither  gain  nor  lose  heat,  on 
account  of  the  small  time  which  each  particle  takes  in  passing  through.  This  being 
the  case,  the  kinetic  energy  of  the  quantity  of  gas  which  passes  a  given  cross-section 
of  the  nozzle  in  a  given  time,  plus  the  work  it  does  in  displacing  the  gas  in  the  region 


p, 


FIG.  10.— Ideal  apparatus  illustrating  the  flow  of  gas  through  a  nozzle 

into  which  it  rushes,  must  be  equal  to  the  loss  in  intrinsic  energy  of  the  gas,  plus  the 
work  done  upon  it  by  the  advancing  mass  of  gas  which  takes  its  place  in  the  region 
from  which  the  gas  flows. 

56.  Flow  through  a  Nozzle.  This  will  be  apparent  from  a  consideration  of 
Fig.  10,  in  which  A  is  a  cylinder  and  B  a  nozzle.  The  cross-section  of  the  nozzle  is 
very  small  in  comparison  with  that  of  the  cylinder,  so  that  the  velocity  of  the  gas 
in  the  cylinder  may  be  neglected.  The  gas  emerging  from  the  nozzle  passes  into 
the  tube  C,  whose  cross-section  is  the  same  as  that  of  the  nozzle  at  the  point  where 
the  nozzle  terminates.  Assume  that  cylinder  A  is  filled  from  point  D  with  gas 
having  a  pressure  PI  and  a  temperature  Tl  and  the  tube  is  filled  to  the  point  E  with 
gas  having. a  pressure  P2  and  a  temperature  T2.  At  E  in  the  tube  and  at  D  in  the 
cylinder  are  pistons,  which,  of  course,  exert  upon  the  gas  a  pressure  equal  to  the 
pressure  exerted  upon  them  by  the  gas.  Since  the  pressure  in  tube  C  is  less  than 
the  pressure  in  cylinder  A,  the  gas  will  flow  from  A  to  C  through  the  nozzle,  and  if 
the  pressure  in  A  and  C  are  to  remain  constant,  the  pistons  must  both  move  to  the 
right.  If  a  certain  quantity  of  gas  be  supposed  to  flow  from  A  to  C  in  one  second, 
then  its  volume  in  A  may  be  assumed  to  be  Vt  and  its  volume  in  C  may  be  assumed 
to  be  T72-  The  amount  of  work  done  by  piston  D  upon  the  gas  during  this  second 


42  THE  EXPANSION  OF  GASES  ART.  57 

is  equal  to  PvVlt  and  the  amount  of  work  done  by  the  gas  upon  the  piston  E  is  P2F2. 
The  intrinsic  energy  of  the  gas  has  been  diminished  by  the  amount 


and  the  kinetic  energy  gained  by  the  gas  is  equal  to 


in  which  W  is  the  weight  of  gas  which  flows  through  the  nozzle  in  one  second,  and 
v  is  the  velocity  of  the  gas  flowing  into  tube  C. 

67.  Determination  of  the  State  of  the  Gas  Passing  the  Throat  of  a  Nozzle. 
At  first  the  gain  in  velocity  as  the  gas  passes  successive  sections  of  the  nozzle  will 
proceed  at  a  greater  rate  than  the  increase  in  the  volume  of  the  mass,  and  the 
successive  sections  will  diminish  in  area,  the  nozzle  being  convergent.  When  a 
certain  point  is  reached,  however,  the  rate  of  gain  in  volume  increases  more  rapidly 
than  the  rate  of  gain  in  velocity,  and  the  nozzle  from  that  point  outward  must  be  made 
divergent.  The  point  of  minimum  cross-section  is  known  as  the  throat  of  the  nozzle, 
and  the  quantity  of  gas  which  the  nozzle  will  pass  will  obviously  depend  upon  the 
area  of  this  cross-section  of  the  nozzle.  Let  v  be  the  velocity  of  the  gas  passing 
this  cross-section,  let  W  be  the  number  of  pounds  passing  this  cross-section  per 
second,  let  T  be  the  absolute  temperature  of  the  gas  passing  this  cross-section,  let 
P  be  the  pressure  of  the  gas  passing  this  cross-section,  and  let  Tl  and  Pt  be  the 
temperature  and  pressure  of  the  gas  entering  the  nozzle.  Then  we  will  have, 
collecting  and  equating  the  terms  given  at  the  end  of  Art.  56, 

T^  v2 

l  *  ~^<T+ 

This  may  be  written 

W  KV(T.-T)  +  W  RTV  =  —.  V-+WR  T,  .     .  (2) 

*9 
collecting,  we  will  have 

»j2 

-T)=~, (3) 


or 


V     f T1          rT1\  fA\ 

K^-T)^-, 

solving 

v  =  A/2  g  K.p(T,  -T)  =  k^T^T (5) 

Also  if  F  =  the  volume  of  W  pounds  of  gas  of   temperature  T  and  pressure  P, 
then 

V -?-¥-*,£ (6) 

y 
The  area  of  the  nozzle  at  any  cross-section  is  — ,  and  therefore  we  may  write 

kT 
a  = , (7) 


The  area  a  will  therefore  be  a  minimum  wheh 

is  a  maximum.        .     . (8) 


\RT.  57  GAS   PASSING   THE   THROAT  OF  A   NOZZLE  43 

From  Art.  44,  equation  (D), 


Substituting  this  in  (8)  we  will  have  the  expression 

-I— 
Pl  Tr-l  \ 


(10) 


Since  P^  and  7\  are  constants,  this  will  be  a  maximum  when 


Tr-l  VTi-T  is  a  maximum (11) 

Squaring,  we  have  the  expression, 

_2_        r+i 

Differentiating  and  equating  to  zero,  we  have 


2  =1         - 

—  l^rr-i-  rr-1-0.  .    '  ......     (13) 

Solving  for  Tlt 


Tr-l 

from  whence  solving  for  T, 


in  which  T  is  the  absolute  temperature  of  the  gas  passing  the  throat  or  minimum 
section  of  the  nozzle.     Now 


Substituting  (15)  in  (16)  we  have, 


_2_m\_L- 

rj.ij  i  ir—  1 


in  which  P  is  the  absolute  pressure  of  the  gas  passing  the  throat  of  the  nozzle,  when 
the  pressure  in  the  region  beyond  the  throat  is  equal  to  or  less  than  the  value  of  P 
given  by  the  above  equation.  If  the  pressure  in  the  region  beyond  is  greater  than 
this  value,  the  nozzle  is  not  of  the  proper  form,  and  our  conclusions  do  not  hold. 
From  (5),  the  velocity  of  the  gas  passing  the  throat  is 


(18) 


which  is  a  fixed  quantity,  if  the  pressure  of  the  region  into  which  the  gas  escapes  is 
less  than 


44  THE  EXPANSION  OF   GASES  ART.  58 

Now  the  volume  of  gas  passing  the  throat  in  one  second  is,  of  course, 

1-       ......     (19) 


also 


Substituting  the  value  of  T  from  (15),  and  of  P  from  (17)  in  (20),  we  will  have 

-2-r, 
v=ws—r—  VRTI 


(20) 


2    ~~IP 


Substituting  (21)  in  (19),  and  solving  for  W  we  have 

^-S'^SM^!)11'  ......  (22) 

Simplifying,  this  becomes 


which,  for  any  particular  gas,  becomes 

(24) 


in  which  kl  is  a  constant  depending  only  on  the  physical  qualities  of  the  gas,  and  is 
found  from  the  expression, 


-J 
'-  \ 


For  air  we  have  k^  =  .526. 

For  any  particular  nozzle  the  equation  becomes 


58.  Actual  Discharge  from  a  Nozzle.  On  account  of  friction,  not  all  of  the 
intrinsic  energy  made  available  by  a  given  fall  in  pressure  can  be  transformed  into 
kinetic  energy.  Hence  the  quantity  of  gas  discharged  from  an  orifice  per  second 
will  be  less  than  is  indicated  by  equation  (23)  in  the  preceding  paragraph.  It  is 
probable  that  the  friction  increases  somewhat  with  the  density  of  the  gas,  and  it 
is  certain  that  it  depends  a  good  deal  upon  the  form  and  workmanship  of  the  nozzle. 
We  may  therefore  write  for  the  quantity  of  gas  discha'ged  per  second  through  any 
orifice,  from  a  region  in  which  the  pressure  is  Pl}  into  another  region  in  which  the 
pressure  is  equal  to  or  less  than 


- 

'Vr+V 

the  equation 


(1) 


ART.  59 


DISCHARGE  AGAINST   HIGH   BACK  PRESSURES 


45 


in  which  TF=the  number  of  pounds  of  gas  discharged  per  second. 

a=the  minimum  area  of  the  orifice  in  square  inches; 

P1=the  absolute  pressure    of    the  gas  in  pounds  per  square  inch  just  pre- 
vious to  entering  the  orifice; 

Tl=  the  absolute  temperature  of  the  gas,  just  previous  to  entering  the  orifice; 
k  =  a   constant   depending   on   the   nature    of   the  gas   and   the  form   and 
smoothness  of  the  orifice,  but  whose  greatest  value  will  be  less  than 
that  of  &J  in  equation  (25)  from  the  preceding  paragraph. 

59.  Discharge  against  High  Back  Pressures.      In  case  the  pressure  in  the 
region  into  which  the  gas  flows  is  greater  than 


i    2    U- 


FIG.  11. — Illustrating  the  flow  of  gas  through  a  convergent  nozzle. 

and  the  orifice  has  no  throat,  being,  for  instance,  of  the  form  shown  in  Fig.  11,  then 
we  will  have  as  before  from  equation  (5),  Art.  57, 


also  from  equation  (6),  Art.  57, 


WRT 


(D 


(2) 


from  which  we  may  write,  since  V^  =  av, 


(3) 


(4) 


46  THE  EXPANSION  OF  GASES  ART.  60 

Substituting  from  equation  (F),  Art.  44,  for  T2,  we  have, 


Clearing  and  simplifying 


2  r  +  l 


^-«^=v^\-s(V)f-«y)  r w 


This  expression  may  be  written  in  the  form 


\    /z±r 

r'-rV    r   '.      .........     (7) 


in  which  W,  a,  P1}  and  7\  are  as  in  equation  (1),  Art.  57, 


Equation  (7),  given  above,  may  be  transformed  into 

/     2r-2    ¥=7          rzJ.     L\ 

(Pi     r    P,r    -P,    r   P2r)  .....     (8) 

It  will  be  noted  that  the  sums  of  the  exponents 


are  unity  in  each  case.  Hence  if  Pl  and  P2  are  not  widely  different  in  value,  we 
may  write  for  the  radical,  without  serious  error,  a  simple  expression  which  trans- 
forms equation  (8)  to 


W  =  fco-y- 


in  which  W,  a,  P2,  and  Pt,  and  7\  are  as  in  equation  (8),  and  k  is  a  constant  to  be 
determined  experimentally.  Fliigner  gives  for  the  value  of  k  for  air  the  figure 
1.06.  The  value  of  this  constant  will,  however,  depend  upon  the  character  of  the 
orifice.  For  any  particular  nozzle  the  equation  becomes 


-»  1 


(10) 


60.  Calibration  of  Orifices  for  the  Measurement  of  Air.  A  method  which 
is  frequently  employed  for  determining  quantities  of  air  is  to  allow  the  air  to  flow 
through  a  nozzle  under  known  conditions.  If  this  nozzle  is  of  the  proper  form  and 
of  first-class  workmanship,  and  its  dimensions  are  accurately  known,  the  quantity 
of  air  flowing  may  be  readily  determined  by  means  of  the  equations  which  have 
been  developed  in  the  preceding  articles.  However,  it  is  often  convenient  to  use 
nozzles  so  small  that  their  exact  measurement  is  difficult,  and  it  is  then  of  importance 


ART.  60 


ORIFICES   FOR  THE   MEASUREMENT  OF  AIR 


47 


to  determine  the  value  of  the  constant  C  in  equation  (26),   Art.  57,  or  equation  (10), 
Art.  59.  This  may  be  done  in  the  following  manner: 

A  receiver,  as  shown  in  Fig.  12,  of  known  volume,  is  filled  with  air  or  other  gas 
at  any  convenient  pressure,  all  means  of  egress  from  the  receiver  being  stopped, 
except  through  the  nozzle  which  is  to  be  tested.  Simultaneous  readings  of  the 
pressure  in  the  receiver,  and  the  temperature  of  the  air  entering  the  nozzle,  are  made 
by  means  of  the  pressure  gage  and  thermometer  shown  in  the  figure  at  regular 
intervals,  say  every  fifteen  seconds.  The  barometer  reading  is  also  noted  during  the 
experiment.  A  smooth  curve  may  now  be  plotted  showing  the  relation  of  the 
pressure  of  the  gas  in  the  receiver  to  the  time,  and  another  showing  the  relation  of 
the  temperature  of  the  gas  in  the  receiver  to  the  time. 


FIG.  12.  —  Reservoir  for  the  calibration  of  air  nozzles. 

If  a  tangent  be  drawn  to  the  time-pressure  curve  at  any  point  we  may,  from  its 
intercepts,  determine  the  value  of  the  differential  -j-.  In  like  manner,  if  a  tangent 
be  drawn  to  the  time-temperature  curve  at  the  corresponding  points,  we  may  deter- 

J/TT 

mine  the  differential  -T-.     During  the  progress  of  the  experiment  the  reservoir  con- 

tains a  variable  quantity  of  gas  under  a  variable  pressure  and  at  a  variable  tem- 
perature, but  the  volume  of  the  gas  and  the  quantity  R  for  the  gas  will  of  course 
be  constant.  We  may  write  from  the  characteristic  equation  of  gases, 


P  = 


Differentiating  this  expression,  we  will  have 


Dividing  this  through  by  dt,  we  will  have 


dt 


48  THE  EXPANSION   OF   GASES  ART.  60 


In  this  equation,  we^may  substitute  for  — r-  and  —rr  their  values  as  obtained  from 

the  tangents  to  the  two  curves,  for  T  the  absolute  temperature  of  the  gas  at  the 
instant  for  which  the  tangents  are  drawn,  and  for  W  the  mass  of  gas  contained 
within  the  reservoir  at  that  instant,  as  computed  from  its  pressure,  volume,  and 

temperature,  and  solve  for  —jr,  which  is  the  rate  of  discharge  of  the  nozzle  at    the 

given  temperature  and  pressure,  and  is  equal  to  the  weight  of  gas  discharged  per 
second.  Substituting  this  value  for  W  in  the  equations 

w  =  c^Ji a) 

or 


W.C^W£K (2) 

and  solving  for  Cl  or  C2  we  may  obtain  the  coefficient  of  the  nozzle.     Equation  (1) 
is  to  be  used  in  case  the  pressure  in  the  reservoir,  Pl}  is  greater  than 


where  P2  is  the  pressure  of  tne  atmosphere.  Equation  (2)  is  to  be  used  in  case  the 
pressure  in  the  reservoir  is  less  than  the  value  given.  Several  computations  may 
be  made  from  one  set  of  observations  and  the  mean  of  the  results  taken  as  the  value 
of  the  coefficient  Cl  or  C2. 

It  is  not  usually  wise  to  depend  upon  the  results  given  by  the  theoretical  equations 
for  the  flow  of  air  through  orifices,  since,  as  it  passes  through  an  orifice,  the  air  stream 
undergoes  a  certain  amount  of  contraction  which  cannot  be  measured  directly.  It 
is  usually  better,  no  matter  what  the  form  of  orifice,  to  determine  its  rate  of  discharge 
experimentally  for  several  different  pressures  and  to  derive  from  these  rates  the 
coefficient  Cl  or  C2  which  can  be  substituted  in  equations  (1)  and  (2)  in  the  pre- 
ceding paragraph. 

PROBLEMS 

1.  A  mass*  of  gas  which  initially  occupies  a  volume  of  2  cu.ft.,  and  has  a  pressure 
of  100  Ibs.  absolute  per  square  inch,  expands  isothermally.     Find  its  pressure  when  its 
volume  becomes  4  cu.ft.     When  it  becomes  6  cu.ft.     When  it  becomes  8  cu.ft. 

Ans.    50,  33£,  and  25  Ibs.  per  square  inch. 

2.  Find  the  volume  of  the  above  mass  of  gas  when  the  pressure  becomes  75  Ibs. 
absolute.     When  it  becomes  40  Ibs.  gage.     When  it  becomes  20  Ibs.  gage. 

Ans.    2.67,  3.66,  and  5.77  cu.ft. 

3.  Draw  the  pressure  volume  curve  of  the  above  mass  of  gas,  making  the  scale 
of  pressures  1  in.  equals  25  Ibs.  per  square  inch,  and  the  scale  of  volumes  1  in.  equals 
1  cu.ft. 

4.  Find  the  work  done  by  the  mass  of  gas  in  Problem  1  in  expanding  from  a 
volume  of  2  cu.ft.  to  a  volume  of  6  cu.  ft.     To  a  volume  of  8  cu.ft. 

Ans.    31,600  and  39,900  ft.-lbs. 

5.  A  Ib.  of  air  at  a  temperature  of  60°  F.  expands  isothermally  from  a  volume  of 
3  cu.ft.  to  a  volume  of  12  cu.ft.     Find  the  work  of  expansion.     Find  the  heat  added. 

Ans.    38,400  ft.-lbs.  and  49.4  B.T.U. 


ART.  60  PROBLEMS  49 

6.  A  Ib.  of  air  expands  adiabatically  and  its  temperature  falls  from  200°  to  100° 
F.     What  is  the  loss  in  intrinsic  energy  in  B.T.U.?     What  is  it  in  ft.-lbs.? 

Ans.    16.867  B.T.U.  and  13,100  ft.-lbs. 

7.  A  quantity  of  air  expands  adiabatically  from  a  pressure  of  100  Ibs.  to  a  pres- 
sure of  25  Ibs.  per  square  inch  absolute.     Its  initial  volume  is  1  cu.ft.     What  is  the 
final  volume.  Ans.    2.68  cu.  ft.  / 

8.  If  the  initial  temperature  of  the  ah-  in  problem  7  were  80°  F.,  what  would  be 
its  final  temperature?  Ans.     —  98°F.    / 

9.  A  mass  of  air  expands  adiabatically  from  a  pressure  of  100  Ibs.     The  ratio  of 
expansion  is  4.     Find  the  final  pressure.  Ans.    14.25  Ibs. 

10.  If  the  initial  temperature  in  Problem  9  were  100°  F.,  find  the  final  temperature. 

Ans.     -142°F. 

11.  A  quantity  of  air  is  compressed  adiabatically  until  its  temperature  rises  from 
530°  absolute  to  1000°  absolute.     If  its  initial  pressure  is  1  atmosphere,  find  its  final 
pressure  in  atmospheres.  Ans.    9.04  atmospheres. 

12.  If  the  initial  volume  of  the  air  in  Problem  11  is  1  cu.ft.,  find  its  final  volume. 

Ans.    .209  cu.ft. 

13.  Find  the  work  done  by  the  expanding  air  in  problem  7. 

Ans.    11,670  ft.-lbs.  / 

14.  One  Ib.  of  air  is  compressed  adiabatically,  and  its  temperature  is  raised  from 
60°  to  250°.     Find  the  work  of  compression.  Ans.     24,900  ft.-lbs. 

15.  Find  the  work  done  by  1  Ib.  of  air  expanding  as  in  Problem  10. 

Ans.    31,700  ft.-lbs. 

16.  Find  the  work  required  to  compress  two  Ibs.  of  air   between  the  temperature 
limits  given  in  Problem  11.  Ans.    462,000  ft.-lbs. 

17.  Compute  the  initial  volume  of  the  air  in  Problem  14,  assuming  that  the  initial 
pressure  is  15  Ibs.  per  square  inch,  and  draw  the  pressure  volume  curve  making  the 
scale  of  pressure  1  in.  equals  15  Ibs.  and  the  scale  of  volumes  1  in.  equals  2  cu.ft. 

18.  One  Ib.  of    air   having  an  initial  volume  of  6  cu.ft.  and  a  pressure  of  30  Ibs. 
per  square  inch  absolute  expands  at  constant  pressure  until  its  volume  is  12  cu.ft. 
Compute  the  initial  and  final  temperatures.  Ans.  ~i#T7  1ufd~562?  F. 

19.  Compute  the  work  of  expansion  in  Problem  18.  Ans.    25,950  ft.-lbs.    „ 

20.  Compute  the  quantity  of  heat  added  to  the  gas  hi  Problem  18. 

Ans.    115.2  B.T.U.  ^ 

21.  Compute  the  increase  in  intrinsic  energy  in  Problem  18.       Ans.    81.9  B.T.U.  ^ 

22.  A  quantity  of  air  expands  and  the  work  of  expansion  is  twice  the  loss  in  in- 
trinsic energy .     Find  the  value  of  the  exponent  N.  Ans.    1.2034. 

23.  Computation  from  the  card  given  by  an  air  compressor  shows  that  the  index 
of  the  compression  line  is  1.35.     Find  the  ratio  of  the  work  performed  to  the  gain 
in  intrinsic  energy.  Ans.    1.162. 

24.  Air  is  compressed  from  a  pressure  of  1  atmosphere  to  a  pressure  of  4  atmos- 
pheres.    The  value  of  the  index  of  polytropic  compression  is  1.25.     Find  the  final  • 
volume  in  per  cent  of  the  initial  volume.  Ans.    33%.    , 

25.  If  the  initial  temperature  in  Problem  24  be  70°  F,  find  the  final  temperature. 

Ans.    240°  F. 

26.  One  pound  of  hydrogen  expands  from  a  volume  of  3  cu.ft.  to  a  volume  of 
10  cu.ft.,    the   index   of   polytropic   expansion    being    1.1.     Find   the   final   absolute 
pressure  in  per  cent  of  the    initial  absolute  pressure.  Ans.    26.6%. 

27.  If  the  initial  temperature  is   1000°  absolute  in  Problem  24,   find   the   final 
absolute  temperature.  Ans.    886°  abs. 

28.  The  initial  pressure  and  volume  of  1  Ib.  of  air  are  10  atmospheres  and  2  cu.ft. 


50  THE  EXPANSION  OF  GASES  ART.  60 

respectively.     Compute  the  pressure  when  the  temperature  has  fallen  to  60°  F.  as 
a  result  of  polytropic  expansion,  the  index  being  1.3.  Ans.    1.555  atmospheres. 

29.  Compute  the  volume  of  the  air  in  Problem  28  when  the  temperature  has  fallen 
to  zero  F.  Ans.    12.50  cu.ft. 

30.  Draw  the  expansion  line  of  the  air  in  Problem  28  taking  for  the  scale  of 
volumes  1  in.  =  2  cu.ft.  and  for  the  scale  of  pressures  1  in.  =  2  atmospheres. 

31.  Compute  the  velocity  of  sound  in  hydrogen  when  the  temperature  of  the  gas 
is  zero  F.  Ans.    4010  ft.  per  sec. 

32.  The  velocity  of  sound  in  air  is  1125  ft.  per  second  at  a  temperature  of  60°  F. 
Compute  the  value   of  f. 

33.  An  explosive  mixture  of  gas  is  confined  at  a  pressure  of  100  Ibs.  per  square 
inch.     After  ignition,  the  pressure  rises  to  300  Ibs.  per  square  inch.     The  temperature 
of  the  gas  is  400°  F.     Find  the  rate  of  propagation  of  the  explosion  wave.     Take  f  as 
1.40,  and  R  as  53.0.  Ans.    2330  ft.  per  sec. 

34.  The  minimum  area  of  a  nozzle  is  1  sq.in.  and  the  velocity  of  the  air  passing 
this  section  is  2000  ft.  per  second.     Find  the  volume  passing  this  section  per  second. 

Ans.    13.9  cu.ft.  per  sec. 

35.  The  temperature  of  the  air  entering  a  nozzle  is  100°  F.     Find  the  temperature 
of  the  air  in  the  throat  of  the  nozzle.  Ans.    5°  F. 

36.  The  pressure  of  the  air  as  it  enters  this  nozzle  is  100  Ibs.  per  square  inch 
absolute.     Find  the  pressure  in  the  throat  of  the  nozzle. 

Ans.    52.5  Ibs.  per  square  inch. 

37.  Find  the  velocity  of  the  air  passing  the  throat  of  the  nozzle  in  Problem  36. 

Ans.    1064  ft.  per  second. 

38.  What  will  be  the  highest  pressure  of  the  air  in  the  region  into  which  the  nozzle 
discharges,  which  will  permit  answers  to  Problems  35-37  to  be  correct? 

Ans.    52.5  Ibs. 

39.  The  area  of  the  throat  in  Problem  36  is  0.001  sq.ft.     Find  the  weight  of  air 
discharged  per  second.  Ans.    0.325  Ibs. 

40.  Find  the  value  of  fct  in  equation  (24),  Art.  57,  for  carbon  dioxide.       Ans.    0.640. 

41.  Find  the  value  of  the  constant  C^  in  equation  (26),  Art.  57,  for  a  nozzle  having 
an  area  of  0.01  sq.in  for  carbon  dioxide. 

Ans.    0.0064  when  Pl  is  in  pounds  per  square  inch  absolute. 

42.  Air  flows  through  a  nozzle  having  an  area  of  0.01  sq.in.  from  a  region  where  the 
pressure  is  100  Ibs.  per  square  inch  into  a  region  where  the  pressure  is  90  Ibs.  per  square 
inch.     The  initial  temperature  is  80°  F.     Find  the  theoretical  rate  of  discharge. 

Ans.    0.0164  Ibs.  per  second. 

43.  Compute  the  value  of  A;  in  equation  (9)  Art.  59,   for  the  conditions  in  Prob- 
lem 42.  Ans.    1.27. 


CHAPTER  IV 
THERMODYNAMIC   PROCESSES  AND  CYCLES 

61.  General  Definitions.     The  thermodynamic  state  of  a  substance  is 
defined  when  its  temperature,  pressure,  density,  mass  and  composition 
are  known. 

A  substance  having  a  definite  mass,  and  of  homogeneous  composition, 
is,  in  thermodynamics  termed  a  body,  no  matter  what  the  physical  state 
of  the  substance  may  be. 

A  body^is  in  thermal  equilibrium  when  every  part  of  it  is  of  the  same 
.temperature. 

A  body  is  in  thermodynamic  equilibrium  when  every  part  of  it  is  of 
the  same  temperature,  pressure,  and  density. 

An  isolated  body  is  one  which  is  so  situated  that  it  neither  gains  nor 
loses  heat. 

An  isolated  system,  usually  termed  simply  a  system,  is  a  group  of 
bodies  so  situated  that  the  system  neither  gains  nor  loses  heat. 

When  a  body  undergoes  a  change  in  thermodynamic  state,  it  is  said 
to  undergo  a  process.  If,  at  every  instant  during  this  process  all  parts 
of  the  body  are  in  thermodynamic  equilibrium,  the  process  is  said  to  be 
reversible.  If  at  any  point  during  the  process  all  parts  of  the  substance 
are  not  of  the  same  temperature,  pressure,  and  density,  the  process  is  said 
to  be  irreversible  or  sweeping.  A  substance  which  undergoes  a  reversible 
process  can  be  brought  back  to  its  initial  state  by  causing  it  to  pass  in  the 
reverse  order  through  each  successive  state  of  the  process.  This  is  called 
reversing  the  process.  A  substance  which  undergoes  a  sweeping  process 
cannot  be  brought  back  to  its  initial  state  by  reversing  the  sweeping 
process. 

62.  Examples  of  Processes.     As  an  example  of  a  reversible  process, 
we  may  take  the  adiabatic  expansion  of  a  gas,  a  process  which  lowers 
its  temperature  and  pressure  and  increases  its  volume.     At  every  instant 
during  the  expansion  every  portion  of  the  gas  has  the  same  temperature, 
pressure,  and  density.     By  raising  the  pressure  upon  the  gas,  its  tem- 
perature and  density  will  be  increased,  and  its  volume  decreased,  and  it 
will  be  brought  back  to  its  initial  state,  after  passing  successively  through 
each  state  through  which  it  passes  during  its  expansion. 

As  an  example  of  a  sweeping  process,  we  may  take  the  case  of  a  body 

51 


52  THERMODYNAMIC   PROCESSES  AND  CYCLES  ART.  63 

of  gas  confined  under  pressure,  which  is  allowed  to  escape  from  the  con- 
taining vessel  through  an  orifice.  While  it  is  escaping,  that  portion  of 
the  gas  which  has  passed  through  the  orifice  will  be  of  a  different  tem- 
perature, pressure,  and  density  from  that  portion  yet  within  the  con- 
taining vessel,  and  the  gas  is  not  in  thermodynamic  equilibrium  during 
the  process.  Neither  is  there  any  possible  method  which  will  enable 
us  to  pass  the  gas  from  a  region  of  low  pressure  back  through  the  orifice 
into  a  region  of  high  pressure,  and  yet  have  it  pass  in  turn  through  the 
several  conditions  through  which  it  passed  during  the  progress  of  the 
sweeping  process,  and  the  process  cannot  be  reversed. 

63.  Cycles.     When  a  substance  is  caused  to  undergo  a  series  of  proc- 
esses, for  any  purpose,  and  is  finally  brought  back  to  the  thermodynamic 
state  which  it  had  initially,  the  substance  is  said  to  perform  a   cycle. 
The  substance  performing  the  cycle  is  called  the  working  substance,  and 
in  case  this  substance  is  a  fluid,  as  it  usually  is,  it  is  called  the  working 
fluid.     In  case  the  series  of  processes  which  the  working  fluid  undergoes 
in  any  cycle  are  all  reversible  processes,  the  cycle  is  said  to  be  reversible, 
or  perfect.      In  case  one  or  more  of  the  processes  are  sweeping  processes, 
the  cycle  is  said  to  be  irreversible,  or  imperfect.     The  purpose  of  causing 
a  working  substance  to  perform  a  cycle  is  usually  either  to  transform  heat 
into  work,  or  to  transfer  heat  from  a  region  of  low  temperature  to  a  region 
of  high  temperature.     A  thermodynamic  machine  in  which  a  cycle  is 
performed  for  the  purpose  of  transforming  heat  into  work    is  called  a 
heat  engine.      A  machine  in  which  a  cycle  is  performed  for  the  purpose 
of  transferring  heat  from  a  region  of  low  temperature  to  a  region  of  high 
temperature  is  called  a  refrigerating  machine. 

64.  Entropy.     It   is   convenient   in  the  development   of  proofs   for 
many  thermodynamic  theorems,  and  in  working  out  certain  classes  of 
problems,  to  make  use  of  a  ratio  or  abstract  quantity,  to  which  the  term 
entropy  has  been  applied. 

The  entropy  of  a  substance  having  a  given  state  may  be  defined  as  the 
sum  of  the  quotients  obtained  by  dividing  the  successive  increments  of 
heat  necessary  to  bring  the  substance  to  the  given  state,  by  the  absolute 
temperature  at  which  each  addition  of  heat  occurred,  the  substance 
being  in  a  state  of  thermodynamic  equilibrium  throughout  the  several 
processes  necessary  to  bring  the  substance  to  its  final  state. 

This  definition  may  be  represented  by  the  equation 


where  N  is  the  entropy  of  the  substance,  AH  represents  an  elementary 
quantity  of  heat  added  to  the  substance,  and  T  is  the  absolute  temperature 
of  the  substance  during  such  addition  of  heat. 


ART.  65  DIMENSIONS  OF  ENTROPY  53 

Were  it  possible  to  compute  the  quantity  of  heat  necessary  to  bring 
a  substance  from  a  temperature  of  absolute  zero  to  any  given  state,  and 
to  know  the  absolute  temperature  at  which  each  successive  addition  of 
heat  occurred,  it  would  be  possible  to  compute  the  absolute  entropy  of 
the  substance.1  Since,  however,  this  is  neither  possible  nor  even  desirable, 
it  is  customary  to  compute  the  change  of  entropy  of  a  substance  in  pass- 
ing from  some  standard  thermodynamic  state  to  any  given  state.  The 
standard  state  is  then  termed  the  state  of  zero  entropy,  or,  for  brevity,  the 
zero  state,  and  the  change  of  entropy  is  termed  the  entropy  of  the  substance. 

It  may  be  that  in  causing  a  substance  to  pass  from  the  zero  state  to 
some  other  state,  heat  must  be  abstracted  instead  of  being  added.  In 
such  a  case,  the  entropy  change  is  negative  and  the  entropy  of  the  sub- 
stance will  be  a  negative  quantity.  The  zero  state  is  usually  so  chosen 
th.at  in  any  series  of  changes  which  the  substance  must  undergo  while 
it  is  the  subject  of  investigation,  the  entropy  will  remain  a  positive 
'  quantity  throughout  this  series  of  changes. 

65.  Dimensions  of  Entropy.     In  dealing  with  entropy,  the  student 
must  bear  in  mind  that  it  is  an  abstract  quantity;   a  mere  ratio,  having 
no  physical  existence.     It  is  of  the  same  dimensions  as  the  angular  func- 
tions, or  any  similar  mathematical  quantity.     It  is  found  by  dividing 
heat,  which  is  energy,  and  whose  dimensions  are  therefore  force  X  distance, 
by  temperature,  which  is  shown  by  the  kinetic   theory  of  gases  to  be 
energy  per  molecule  (see  Chapter  XXVI.),  and  whose  dimensions  are  also 
therefore  force  X  distance.     It  follows  therefore  that  entropy  is  without 
physical  dimensions,  or,  as  we  say,  it  is  an  abstract  quantity. 

66.  Proposition  I.     The  entropy  of  a  system  is  equal  to  the  sum  of  the. 
entropies  of  the  several  bodies  composing  the  system.   Let  the  system  consist 
of  several  bodies  and  also  let  it  have  the  zero  state  when  each  of  the 
bodies  composing  it  has  the  zero  state.     To  bring  the  system  from  the 
zero  state  to  a  given  state,  it  is  necessary  to  bring  each  of  the  bodies 
composing  it  from  the  zero  state  to  a  given  state.     In  doing  so,  it  is 
necessary  to  make  to  each  body  certain  heat  additions  at  certain  tem- 
peratures, thereby  increasing  the  entropy  of  the  body  by  a  definite  amount. 
Since  these  heat  additions  are  also  made  to  the  system  at  these  same 
temperatures,  the  entropy  of  the  system  has  been  increased  by  the  same 
amount.     Obviously,  then,  the  amount  by  which  the  entropy  of  the  sys- 
tem will  be  increased  will  be  the  sum  of  the  amounts  by  which  the  entropies 
of  the  several  bodies  are  increased,  or  the  entropy  of  the  system  is  the  sum 
of  the  entropies  of  the  several  bodies  composing  it. 

67.  Proposition  II.     The  entropy  of  an  isolated  system  which  remains 
continuously  in  thermodynamic  equilibrium   is   a  constant  quantity.     This 
follows  from  the  fact  that  in  order  to  change  the  entropy  of  a  body  or  of 

1  The  absolute  entropy  of  a  body  is  always  infinity. 


54  THERMODYNAMIC   PROCESSES  AND  CYCLES  ART.  68 

/ 

a  system,  heat  must  be  added  to  or  abstracted  from  the  body  or  system. 
Since  heat  cannot  be  added  to  or  abstracted  from  an  isolated  system,  its 
entropy  will  remain  unchanged,  provided  that  it  remains  continuously 
in  thermodynamic  equilibrium. 

68.  Proposition  III.     The  entropy  of  a  body  is  unchanged  by  causing 
it  to  complete   a  reversible  cycle.     This  will  be  apparent  from  the  follow- 
ing  considerations.     Assume   an   isolated   system1  composed   of  severs 
bodies,  each  one  having  a  definite  entropy.     Let  us  assume  that  one  of 
these  bodies  is  caused  to  complete  a  reversible  cycle,  during  which  it, 
and  all  other  bodies  of  the  system,  remain  continuously  in  thermodynamic 
equilibrium.     At  the  completion  of  this  cycle,  assume  that  the  body  is 
taken  from  the  system  and  replaced  by  a  body  identical  with  it  in  every 
respect  (i.e.,  having  the  same  thermodynamic  state)  but  having  the  same 
entropy  as  the  body  which  was  taken  away  originally  had.     In  taking 
this  body  from  the  system  and  replacing  it  with  an  identical  one,  heat 
is  neither  added  to  nor  abstracted  from  the  system,  and  the  entropy 
of  the  system  remains  unchanged.     Therefore  the  entropy  of  the  body 
taken  from  the  system  must  be  the  same  as  the  entropy  of  the  body  intro- 
duced into  the  system.     Hence,  after  undergoing  any  series  of  reversible 
processes  and  returning  to  its  original  state,  the  entropy  of  a  body  will 
be  unchanged. 

69.  Proposition  IV.     The  entropy  of    a    body  is  independent  of   the 
number  and  kind  of  reversible  processes  to  which  it  may  have  been  subjected 
in  bringing  it  to  a  given  state.     Assume  a  body  having  the  state  indicated 
by  A  in  Fig.  13.  Assume  that  it  passes  by  route  c  to  state  B,  route  c  being 

y  composed    exclusively    of    reversible 

processes.  Assume  that  it  is  brought 
back  to  state  A  by  route  d,  also  com- 
posed exclusively  of  reversible  proc- 
esses. The  entropy  of  the  body  is  the 
same  at  the  end  as  at  the  beginning 
of  the  cycle.  The  entropy  of  the  body 
at  state  B  is  equal  to  the  entropy 
at  the  beginning  plus  the  entropy 
gained  during  the  series  of  processes  c. 
The  entropy  of  the  body  at  the  end 
T  of  the  cycle  is  equal  to  the  entropy 


FlG  13  at   state   B   minus   the    entropy  lost 

during  the  series  of  processes  d.     It 

therefore  follows  that  the  entropy  which  would  be  gained  in  passing 
from  state  A  to  state  B  by  route  d,  is  equal  to  the  entropy  gained  in 
passing  by  route  c,  since  the  entropy  gained  in  passing  from  A  to  B  by 
route  d  is  equal  to  the  entropy  lost  in  passing  from  B  to  A  by  the  same 


-RT.  70  ENTROPY  OF  A  SYSTEM  55 

route,  and  this  in  turn  is  equal  to  the  entropy  gained  in  passing  from  A 
to  B  by  route  c.  As  the  only  conditions  imposed  were  that  each  route 
should  be  a  series  of  reversible  processes,  it  follows  that  the  entropy 
gained  in  passing  from  A  to  B  will  be  the  same,  whatever  the  series  of 
eversible  pro-cesses  employed. 

70.  Proposition  V.     The  entropy  of  a  body  depends  upon  its  state  and 
it  therefore  is  independent  of  the  processes,  reversible  or  otherwise,  by  means 
of  which  it  has  been   brought   to   that   state.     This  may  be  demonstrated 
as  follows  :     Assume  a  system  of  bodies  all  of  which  are  in  the  zero  state, 
and  assume  that  one  body  is  caused  to  pass  by  any  series  of  processes, 
reversible  or  otherwise,  to  any  given  state,  A.     Assume  that  a  body, 
identical  in  .mass  and  composition  with  the  one  considered,  is  brought 
from  the  zero  state  to  state  A  by  a  series  of  reversible  processes.     Its 
entropy  will  then  be  a  definite  quantity.     If  this  second  body  be  sub- 
stituted for  the  first,  the  entropy  of  the  system  will  remain  unchanged, 
and  therefore  the  entropy  of  the  body  withdrawn  is  the  same  as  the  entropy 
of  the  body  substituted.     Hence  the  entropy  of  the  body  withdrawn  de- 
pends upon  its  state,  and  not  upon  its  previous  history. 

71.  The  Entropy  of  a  System  is  Increased  by  a  Heat  Transfer.     When 
two  bodies  of  different   temperatures  composing  an  isolated  system  are 
so  placed  that  heat  may  pass  from  one  to  the  other,  it  will,  by  definition 
(see  Art.  15)  pass  from  the  hotter  to  the  colder  body.     The  amount  of 
heat  gained  by  the  latter  is  equal  to  the  amount  of  heat  lost  by  the  former. 
Let  us  call  the  temperature  of  the  hot  body  T\,  and  that  of  the  cold  body 
T2,  and  the  quantity  of  heat  transferred  H.     Then  as  a  result  of  the  heat 
transfer,  the  entropy  of  the  hot  body  will  be  diminished  by  the  amount 


and  the  entropy  of  the  colder  body  will  be  increased  by  the  amount 

H 


Since  the  latter  quantity  is  greater  than  the  former  (its  denominator 
being  less  than  the  denominator  of  the  former  quantity,  while  the  numer- 
ators are  equal),  the  entropy  of  the  system  has  been  increased.  We 
may  therefore  state  that  when  a  heat  exchange  occurs  between  bodies  of 
different  temperatures  composing  a  system,  the  entropy  of  the  system 
is  thereby  increased. 

72.  The  Entropy  of  a  System  is  Increased  by  a  Sweeping  Process. 
When  a  body  of  a  system  undergoes  a  sweeping  process,  the  entropy 


56  THERMODYNAMIC   PROCESSES   AND   CYCLES  ART.  73 

of  the  system  is  thereby  increased.  A  body  which  undergoes  a  sweeping 
process  must  suffer,  as  a  result,  a  change  in  temperature  and  pressure, 
in  temperature  and  volume,  in  pressure  and  volume,  or  in  all  three. 
If  the  body  undergoes  a  change  in  temperature  and  pressure,  its  volume 
remaining  unchanged,  it  must  either  have  heat  added  to  it  or  have  heat 
taken  away  from  it.  In  either  case,  heat  must  be  transferred  from  a 
region  of  high  temperature  to  a  region  of  low  temperature,  and  the  proc- 
ess will  result  in  an  increase  in  the  entropy  of  the  system. 

In  case  the  body  suffers  a  change  in  volume  and  pressure  as  a  result 
of  a  sweeping  process,  the  final  volume  must,  of  necessity,  be  greater  than 
the  initial  volume.  In  order  to  return  the  body  to  its  initial  state,  work 
must  be  done  upon  it  and  heat  extracted  from  it.  The  amount  of 
heat  so  extracted  divided  by  the  absolute  temperature  of  the  body 
measures  the  increase  in  entropy  of  the  system  resulting  from  the  sweeping 
process. 

In  case  the  temperature  and  volume  of  the  body  are  increased,  the 
pressure  remaining  constant,  heat  must  be  added  to  the  body  by  some 
body  having  a  higher  temperature  with  resulting  increase  in  the  entropy 
of  the  system.  In  case  the  temperature  and  volume  are  diminished 
heat  must  be  abstracted  from  the  body  by  some  body  having  a  lower 
temperature  with  resulting  increase  in  the  entropy  of  the  system. 

In  case  a  body  undergoes  a  simultaneous  change  of  pressure,  temper- 
ature and  volume,  the  entropy  must  be  increased,  since  this  change  will 
be  the  equivalent  of  two  changes,  either  one  of  which  will  increase  the 
entropy  of  the  system. 

It  therefore  follows  that  when  a  sweeping  change  occurs  within  a 
system,  the  entropy  of  the  system  is  thereby  increased. 

73.  The  Entropy  of  a  System  Cannot   be  Diminished.     It   follows 
from  the  facts  which  we  have  been  developing  in  regard  to  entropy,  that 
the  entropy  of  a  system  can  never  be  diminished,  but  must  continually 
increase  as  the  bodies  of  the  system  undergo  sweeping  processes.     This 
is  another  way  of  stating  the  well-known  truth  that  all  forms  of  energy 
tend  to  become  heat  and  that  heat  tends  to  distribute  itself  until  all  bodies 
have  the  same  temperature.   A  recognition  of  these  facts  is  so  fundamental 
to  the  science  of  thermodynamics  that  some  form  of  statement  of  them 
is  usually  called  the  second  law  of  thermodynamics,  the  so-called  first 
law  of  thermodynamics  being  a  statement  of  the  interrelation  of  heat  and 
other  forms  of  energy. 

74.  The  Carnot  Cycle.     The  simplest   form  of  reversible  cycle  is  that 
devised  by  the   French  engineer  Carnot,   and  known  therefore  as  the 
Carnot  cycle.     In  the  Carnot  cycle,  the  working  substance  undergoes  the 
four  reversible  processes  indicated  in  the  diagram  in  Fig.  14.     First,  the 
substance  is  caused  to  expand  isothermally  at  some  temperature  T\,  from 


ART.  75 


THE  CARNOT  ENGINE 


57 


state  1  to  state  2.     It  is  then  caused  to  expand  adiabatically  from  state 
2  to  state  3,  thereby  attaining  some  lower  temperature  T2.     It  is  then 
compressed  isothermally  to  state  3  and  finally  compressed  adiabatically 
until  it  reaches  its  initial  state.     Since 
the  several   reversible    processes  may 
be  passed   through   in  reverse   order, 
the  cycle   itself  is  a  reversible   cycle. 
75.  The  Carnot  Engine.     In  order 
to  understand  Carnot's   cycle,  it  will 
be  well   to  devise   an   imaginary  ap- 
paratus capable  of  working  upon  this 
cycle.     Such  an  apparatus,  illustrated 
in  Fig.   15,  will  consist  of  a   cylinder 
of  some   non-conducting   material  in 
which  moves    a   piston    operating    a 

slider-crank  mechanism.  The  head  of  the  cylinder  is  made  of  some 
material  which  is  a  good  conductor  of  heat.  The  space  between  the 
piston  and  cylinder  head  is  occupied  by  the  working  substance,  which 
will  have  at  the  beginning  of  the  cycle  a  temperature  T\.  A  large  hot 
body  of  the  same  temperature,  which  acts  as  a  source  of  heat,  and 


FIG.  14. 


Non 
Conductor 


1 


Cooler 


Heater 


FIG.  15. — Carnot's  engine. 

which  is  called  the  heater,  is  applied  to  the  conducting  head  of  the  cylinder, 
and  the  working  substance  allowed  to  expand.  The  temperature  is  thereby 
lowered  an  infinitesimal  amount,  and  heat  will  immediately  flow  from 
the  heater  into  the  working  substance,  in  order  to  maintain  the  temperature 
at  the  value  T\.  After  the  expansion  has  proceeded  sufficiently,  the 
heater  is  removed  and  replaced  by  a  non-conductor  of  heat.  As  the 


58  THERMODYNAMIO   PROCESSES  AND  CYCLES  ART.  76 

working  substance  continues  to  expand,  and  as  no  heat  is  supplied,  the 
temperature  now  begins  to  fall.  When  this  adiabatic  expansion  has 
proceeded  until  the  temperature  reaches  the  value  T2,  a  body  having  the 
temperature  T2,  and  which  acts  as  a  cooler,  is  applied  to  the  conducting 
head  of  the  apparatus,  and  the  substance  is  compressed.  As  a  result, 
its  temperature  will  be  raised  by  an  infinitesimal  amount,  and  heat  will 
flow  from  the  working  substance  into  the  cooler,  maintaining  the  tem- 
perature of  the  working  substance  constant,  at  the  value  T2.  When 
the  isothermal  compression  has  proceeded  sufficiently,  the  cooler  is 
replaced  by  the  non-conducting  substance  and  the  working  substance  is 
compressed  adiabatically  to  its  initial  state. 

76.  Efficiency  of  the  Carnot  Cycle.     During  the  isothermal  expansion, 
a  quantity  of  heat  H  i ,  whose  amount  depends  upon  the  mass  of  the  work- 
ing substance  and  the  amount  of  expansion  which  it  undergoes,  is  imparted 
to  the  working  substance.     During  isothermal  compression,  a  quantity 
of  heat  H2  is  abstracted  from  the  working  substance.     The  amount  of 
work  performed  by  the  substance  upon  the  piston  of  the  engine  is  obviously 
equal  to  the  mechanical  equivalent  of  the  difference  between  the  heat 
supplied  and  the  heat  abstracted.     The  efficiency  of  the  apparatus  is 
therefore  given  by  the  expression, 

Hl-H2 
H, 

During  this  cycle  the  entropy  of  the  system  remains  constant,  since 
the  cycle  is  composed  exclusively  of  reversible  processes  and  the  system 
remains  continuously  in  thermodynamic  equilibrium.  Since  the  working 
substance  completes  a  perfect  cycle,  its  entropy  at  the  end  of  the  cycle 
is  the  same  as  at  the  beginning.  Hence  the  entropy  lost  by  the  heater 
must  be  equal  to  the  entropy  gained  by  the  cooler.  The  entropy  lost 

TT  TT 

by  the  heater  is  7^.      The  entropy  gained  by  the  cooler  is  7=-.     Writing 
1 1  ±2 

them  equal,  we  have 

H\  _  H2 
Ti  ==  7Y 

Hence,  we  will  have  for  the  efficiency  of  the  cycle 
7?  _  Hi  —  H2  _  T\—  T2 

Hi    -  Yf  ™—      . 

HI  1 1 

It  will  now  be  shown  that  no  engine  can  be  more  efficient  than  a  Carnot 
engine  acting  within  the  same  temperature  range. 

77.  The  Efficiencies  of  Other  Cycles.     If  a  Carnot  engine  be  driven 
backward,  it  will  act  as  a  refrigerating  machine,  taking  heat  from  the 
cooler,  and  adding  to  the  heater  a  quantity  of  heat  equal  to  that  taken 


ART.  77  THE  EFFICIENCIES  OF  OTHER  CYCLES  59 

from  the  cooler  plus  the  heat  equivalent  of  the  work  supplied.  Assume 
an  engine  operating  by  a  cycle  having  a  greater  efficiency  than  a  Carnot 
cycle.  If  this  engine  does  the  same  work,  it  will  be  able  to  drive  the 
Carnot  engine  backward.  The  Carnot  engine  will  then  extract  from  the 
cooler  more  heat  than  is  given  to  it  by  the  engine  assumed,  and  will  give 
off  to  the  heater  more  heat  than  is  taken  from  it  by  the  engine  assumed. 
The  amount  of  heat  lost  by  the  cooler  at  the  low  temperature  T2  will  be 
equal  to  the  amount  of  heat  gained  by  the  heater  at  the  high  temperature 
TI,  and  the  entropy  of  the  system  will  be  diminished.  Since  this  is 
impossible,  it  follows  that  no  cycle  can  be  more  efficient  than  Carnot  's 
cycle. 

In  like  manner,  it  may  be  shown  that  no  reversible  cycle  can  be  less 
efficient  than  Carnot's  cycle,  for  then  Carnot's  cycle,  doing  the  same 
work,  can  drive  this  cycle  backward,  transfer  heat  from  the  cooler  to  the 
heater,  and  so  decrease  the  entropy  of  the  system,  which  is  impossible. 

No  imperfect  cycle  can  be  as  efficient  as  Carnot's  cycle,  since  the  result 
of  a  sweeping  process  is  to  increase  the  entropy  of  the  system  in  which  it 
occurs.  At  the  end  of  such  a  cycle,  the  entropy  of  the  working  substance 
is  the  same  as  at  the  beginning  of  the  cycle,  since  the  working  substance 
has  the  same  thermodynamic  state.  The  entropy  of  the  heater  will, 
of  course,  be  diminished,  and  the  entropy  of  the  cooler  increased.  Since 
the  entropy  of  the  system  is  made  greater  by  the  cycle,  the  gain  in  entropy 
of  the  cooler  is  greater  than  the  loss  in  entropy  of  the  heater.  The  loss 
in  entropy  of  the  heater  will  be 

HJL 
TI 

The  gain  in  entropy  of  the  cooler  will  be 


The  efficiency  of  the  cycle  will  be 

H\  —  PI  2 

Hi 

TT  TJ 

and  since  •—  is  greater  than  -^  it  must  follow  that  the  efficiency  of  this 
^2  ^  i 

cycle  is  less  than 

T,-T2 


. 
We  may  therefore  conclude  the  following  in  regard  to  the  efficiency 

of  heat  engines:     First,  all  heat  engines  operating  on  perfect  cycles  have 
the  same  efficiency  for  the  same  temperature  conditions.     Second,  the 


60  THERMODYNAMIC   PROCESSES  AND   CYCLES  ART.  78 

higher  the  temperature  at  which  the  engine  receives  heat,  and  the  lower 
the  temperature  at  which  it  rejects  heat,  the  greater  the  efficiency  of  the 
engine.  Third,  no  engine  operating  on  an  imperfect  cycle  can  be  as 
efficient  as  an  engine  operating  on  a  perfect  cycle.  Fourth,  it  will  be 
noted  that  in  our  discussion  of  the  Carnot  cycle  and  of  other  cycles, 
no  assumptions  were  made  in  regard  to  the  nature  of  the  working 
substance,  hence  the  efficiency  of  an  engine  operating  by  a  perfect  cycle 
is  independent  of  the  nature  of  the  working  substance,  and  depends 
only  on  the  temperature  limits  between  which  the  engine  operates.  From 
the  equation  giving  the  efficiency  of  a  reversible  cycle,  it  will  be  seen  that 
the  only  method  by  which  we  may  increase  the  efficiency  of  such  a  cycle 
is  by  increasing  the  temperature  at  which  it  receives  its  heat,  or  by  decreas- 
ing the  temperature  at  which  it  rejects  its  heat.  Fifth,  the  efficiency 
of  an  imperfect  cycle  may  depend  on  the  nature  of  the  working  substance. 

78.  The  Efficiency  of  the  Thermo-couple.  It  is  known  that  if  two  unlike  metal 
rods  be  joined  at  two  points  and  one  junction  heated  while  the  other  junction  is  cooled, 
an  electromotive  force  is  produced,  and  a  current  is  caused  to  pass  through  the  rods. 
Such  a  device  is  known  as  a  thermo-couple.  The  passage  of  the  current  through 
the  cold  junction  tends  to  heat  it  while  the  passage  of  the  current  through  the  hot 
junction  tends  to  cool  it.  Heat  must  therefore  be  supplied  to  the  hot  junction  to 
maintain  its  temperature,  and  abstracted  from  the  cold  junction  for  the  same  reason. 
The  quantity  of  electrical  energy  generated  is  equal  to  the  quantity  of  heat  supplied 
to  the  hot  junction  less  the  quantity  of  heat  rejected  by  the  cold  junction.  The 
thermodynamic  efficiency  of  the  apparatus  is  the  same  as  that  of  any  reversible  cycle, 
namely, 


where  Tl  is  the  temperature  of  the  hot  junction  and  T2  is  the  temperature  of  the  cold 
junction.  Were  this  not  so,  such  an  apparatus  could  be  made  to  drive  a  Carnot 
engine  backward  or  be  operated  as  a  refrigerating  machine  by  a  Carnot  engine, 
according  as  it  is  more  or  less  efficient  than  the  Carnot  engine,  and  so  transfer  heat 
from  the  cooler  to  the  heater.  Such  an  action  is  impossible,  since  it  would  decrease 
the  entropy  of  the  system.  It  will  thus  be  seen  that  the  thermo-electric  couple 
obeys  the  same  laws  as  does  any  thermodynamic  engine,  and,  by  a  similar  process 
of  reasoning,  it  may  be  shown  that  any  method  of  transforming  heat  into  work  must 
also  obey  these  laws. 

79.  The  Vital  Processes  not  Thermodynamic.  In  the  bodies  of  animals,  the 
potential  chemical  energy  of  food  is  transformed  into  mechanical  work  by  some 
method  at  present  unknown  to  us.  Since  the  temperature  of  all  parts  of  an  animal 
body  is  constantly  maintained  at  or  about  98°  F.,  and  there  can  be  no  appreciable 
difference  of  temperature  in  the  different  parts,  the  energy  of  the  food  is  not  trans- 
formed into  heat  before  being  transformed  into  mechanical  energy,  but  is  transformed 
into  work  by  some  process  which  is  not  thermodynamic  in  its  nature.  Experiment 
shows  us  that  the  efficiency  of  an  animal  as  a  machine  for  the  transformation  of 
potential  chemical  energy  into  mechanical  energy  ranges  from  30  to  50  per  cent,  which 
is  a  much  greater  efficiency  than  it  is  possible  to  realize  by  any  machine  man  has  as 


ART.  79 


THE   REGENERATOR 


61 


yet  constructed.  Were  it  possible  to  discover  the  method  by  which  chemical  energy 
is  transformed  in  the  animal  body,  we  might  build  machines  of  much  greater  efficiency 
than  those  we  now  possess,  but  obviously  they  would  not  be  thermodynamic  machines. 

80.  The  Regenerative  Principle.  In  certain  kinds  of  engineering 
apparatus,  whose  various  parts  taken  together  form  a  system,  it  is 
often  useful  to  make  use  of  a  principle  termed  regeneration.  Regenera- 
tion is  the  storage  of  heat  in  some  conducting  body,  the  heat  being  taken 
from  some  substance  which  is  being  rejected  from  the  system,  and  sub- 
sequently imparted  to  some  substance  which  is  being  introduced  into  the 
system.  As  an  example  of  the  use  of  the  regenerator,  we  may  take  the 
method  employed  in  steel  works  in  saving  the  heat  which  would  be  other- 
wise lost  from  open-hearth  furnaces.  In  Fig.  16,  A  is  the  combustion 
chamber  of  such  a  furnace.  In  this  combustion  chamber  highly  heated 
gas  and  air  are  brought  together,  and  the  resulting  combustion  still 


FIG.  16. — Regenerative  Furnace. 

further  increases  their  temperature.  The  current  of  gas  and  air  being 
from  the  left  to  right,  it  will  leave  the  combustion  chamber  and  pass  through 
the  chamber  B,  which  is  filled  with  brick  checker  work  (i.e.,  brick  work 
built  up  in  such  a  way  as  to  afford  passage  for  the  gases) .  In  their  passage 
through  this  checker  work  the  gases  heat  the  brick,  that  part  of  the  checker 
work  near  the  furnace  chamber  being  brought  almost  to  the  tempera- 
ture of  the  furnace  and  that  part  near  the  breeching  into  the  which 
gases  pass,  being  warmed  somewhat.  Were  the  gases  allowed  to  pass 
for  a  considerable  length  of  time  in  this  direction,  the  whole  of  the  checker 
work  would  eventually  reach  the  temperature  of  the  furnace,  but  they  are 
not  allowed  to  pass  through  for  any  considerable  period.  After  a  few 
minutes,  the  direction  of  the  current  of  gases  through  the  apparatus  is 
reversed,  gas  and  air  passing  through  the  checker  work  from  right  to  left, 
into  the  combustion  chamber,  where  they  are  burned  and  then  pass  out, 
heating  the  checker  work  in  chamber  C.  The  gases  which  enter  the  checker 
work  in  chamber  B  have  their  temperature  slightly  raised  by  the  first 
bricks  which  they  encounter.  As  they  progress  from  right  to  left  they 
continue  to  receive  heat,  since  they  encounter  hotter  and  hotter  brick 


62  THERMODYNAMIC   PROCESSES  AND   CYCLES  ART.  81 

in  their  progress,  and  at  length  they  enter  the  combustion  chamber  at 
almost  the  temperature  of  the  chamber.  By  this  means  we  are  enabled 
to  maintain  a  very  high  temperature  in  the  combustion  chamber  without 
rejecting  gas  of  a  high  temperature,  which  would  entail  very  great  heat 


If  an  engine  be  caused  to  work  by  a  cycle  in  which  the  working  sub- 
stance is  transferred  from  a  region  of  high  temperature  to  a  region  of  low 
temperature,  passing  through  a  regenerator  on  the  way,  the  cycle  is  said 
to  be  a  regenerator  cycle.  Such  cycles  may  be  made  to  have  very  high 
efficiencies,  approaching,  in  fact,  the  efficiency  of  the  Carnot  cycle.  An 
example  of  such  a  cycle  is  given  in  the  description  of  the  Stirling  hot-air 
engine  in  Chapter  XVIII. 

81.  Pseudo-Cycles.  In  most  practical  thermodynamic  machines  the  working 
substance  is  rejected  from  the  cylinder  or  working  chamber  during  some  portion  of 
the  cycle,  and  is  replaced  by  a  fresh  portion  of  working  substance  during  some  other 
portion  of  the  cycle.  Since  the  working  substance  is  not  returned  to  its  original 
state,  it  will  be  apparent  that  it  does  not  undergo  a  true  cycle,  but  merely  a  series  of 
processes.  Such  a  series  of  processes  may  be  termed  a  pseudo-cycle.  It  may  be  that 
the  Watt  diagram  of  such  a  series  of  processes  can,  in  theory,  be  reproduced  exactly 
by  causing  a  definite  mass  of  working  substance  to  undergo  a  cycle  while  it  remains 
continuously  within  the  working  chamber.  If  such  is  the  case,  the  pseudo-cycle 
is  the  exact  equivalent  of  a  true  cycle  and  may,  in  the  thermodynamic  computation,  be 
treated  as  such.  The  Otto  gas  engine  cycle  (see  Chapter  XIX.)  is  a  cycle  of  this  type. 
On  the  other  hand,  however,  the  series  of  processes  is  often  of  such  a  nature  that  its 
Watt  diagram  cannot  be  reproduced  within  a  working  chamber  containing  a  constant 
mass  of  working  fluid,  and  it  is  not  equivalent  to  a  true  cycle.  Most  practical  cycles 
are  of  this  type,  and  an  important  class  of  thermodynamic  machines,  usually  termed 
gas  compressors,  invariably  operate  upon  such  pseudo-cycles.  They  are  employed 
for  the  purpose  of  transferring  fluid  from  a  region  of  low  pressure  to  a  region  of 
high  pressure,  and  the  rejection  of  the  working  fluid  during  some  portion  of  the  cycle, 
and  its  replacement  by  a  fresh  charge,  is  an  essential  process  of  the  machine. 

An  example  of  a  perfect  cycle  has  already  been  given  in  the  case  of  the  Carnot 
cycle.  The  Otto  gas  engine  cycle,  described  in  Chapter  XIX.,  is  an  illustration  of  an 
imperfect  cycle.  The  Stirling  hot-air  engine  described  in  Chapter  XVIII.,  is  an 
example  of  the  use  of  the  regenerator  cycle.  The  ordinary  air  compressor  described  in 
Chapter  XXII.  is  an  example  of  a  pseudo-cycle. 

PROBLEMS 

1.  Twenty  B.T.U.   are  imparted  to  a  substance  whose  absolute  temperature  is 
1000°.     How  much  is  its  entropy  increased?  Ans.     0.02. 

2.  10.592  B.T.U.  are  imparted  to  a  substance  whose  temperature  is  70°  F.     By 
what  amount  is  its  entropy  increased?  Ans.     0.02. 

3.  The  specific  heat  of  a  substance  is  unity.     One  pound  of  it  is  raised  in  tem- 
perature from  500°  absolute  to  600°  absolute.     What  is  its  increase  in  entropy? 

Ans.     0.1823. 

4.  The  specific  heat  of  a  substance  is  0.2  and  its  mass  is  10  Ibs.     By  how  much  was 
its  entropy  increased  in  raising  it  from  60°  to  80°  F.?  Ans.     0.0784. 


ART.  81  PROBLEMS  63 

5.  Two  pounds  of  water,  1  Ib.  of  which  has  a  temperature  of  500°  absolute  and 
the  other  of  which  has  a  temperature  of  600°  absolute  are  mixed  together.     How 
much  is  the  entropy  of  the  system  increased?     (Assume  the  specific  heat  of  water  to  be 
unity.)  Ans.     0.0083. 

6.  One  pound  of  air  is  confined  in  a  volume  of  1  cu.ft.  at  a  temperature  of  500° 
absolute.     It  is  allowed  to  expand  suddenly  to  a  volume  of  3  cu.ft.  without  doing 
work.     What  quantity  of  work  must  be  done  upon  it  to  return  it  by  isothermal  com- 
pression to  its  initial  state?  Ans.     29,300  B.T.U. 

7.  How  many  B.T.U.  must  be  taken  from  it  during  this  process? 

Ans.     37.69  B.T.U. 

8.  What  was  the  increase  in  entropy  resulting  from  the  sudden  expansion? 

Ans.     0.07538. 

9.  A  Carnot  cycle  engine  takes  heat  at  300°  F.  and  rejects  it  at  80°  F.     What 
is  its  efficiency?  Ans.     29%. 

10.  The  working  fluid  in  the  above  engine  is  1  Ib.  of  air  whose  initial  volume  is 
2  cu.ft.     Find  its  volume  at  the  beginning  of  adiabatic  compression. 

Ans.     4.66  cu.ft. 

11.  The  ratio  of  isothermal  expansion  in  this  cycle  is  2.     Find  the  volume  of  the 
air  at  the  end  of  adiabatic  expansion.  Ans.     9.32  cu.ft. 

12.  What  quantity  of  heat  was  imparted  to  the  air  during  isothermal  expansion? 

Ans.     36.1  B.T.U. 

13.  What    quantity    of   heat    was   rejected    by   the   air  during   isothermal  com- 
pression? Ans.  25.7  =  B.T.U. 

14.  What  quantity  of  work  was  done  by  the  engine  during  the  cycle? 

Ans.     8030  ft.-lbs. 

(Note  the  relation  between  the  heat  supplied  and  the  heat  rejected  and  the  work 
done  and  also  between  the  heat  supplied,  the  work  done  and  the  efficiency.) 

15.  The  hot  junction  of  a  thermo-couple  is  maintained  at  a  temperature  of  400°  F. 
and  the  cool  junction  at  a  temperature  of  32°  F.     What  is  the  efficiency  of  the  couple? 

Ans.     32.8%. 

16.  The  average  temperature  of  the  waste  gases  entering  a  regenerator  is  1200°  F. 
The  average  temperature  of  the  air  drawn  from  the  regenerator  is   1100°  F.     The 
temperature  of  the  air  entering  the  regenerator  is  60°  F.     Find  the  efficiency  of  the 
regenerator.  Ans.     91.2%. 


CHAPTER  V 


THE   THERMAL   PROPERTIES   OF   VAPORS 

82.  The  Effects  of  the  Addition  of  Heat  to  Water.  A  vapor  has  been 
defined  in  Art.  23,  as  an  elastic  fluid  which  may  be  readily  condensed  into 
a  liquid  by  a  slight  reduction  in  temperature.  We  may  best  understand 
the  constitution  of  vapors  if  we  study  the  manner  of  their  formation,  and 

for  this  study  we  will  take  steam  as  a 
typical  vapor.  Assume  that  we  have 
confined  in  the  apparatus  illustrated  in 
Fig.  17,  which  is  identical  with  the  ap- 
paratus previously  described  in  Art.  24, 
one  pound  of  pure  water  at  a  tempera- 
ture of  32°  F.  This  water  will  be  found 
to  occupy  a  volume  of  0.01603  cubic 
feet.  We  will  assume  that  there  is  placed 
upon  the  piston  a  weight  of  2116.3 
pounds,  which,  of  course,  produces  a 
pressure  of  one  atmosphere.  If  heat  be 
applied  to  the  apparatus  it  will  be  found 
that  the  water  increases  in  temperature 
and  expands  slightly  in  volume.  When 
180  B.T.U.  have  been  added  to  the  water, 
it  will,  of  course,  have  a  temperature  of 
212°  F.,  and  its  volume  will  be  0.0168 
cubic  feet. 

If  we  then  continue  to  add  heat  to 
the  water  we  will  find  that  its  tem- 
perature no  longer  rises,  but  that  some 
of  it  is  changed  into  an  elastic  fluid, 

which  we  term  steam.  The  temperature  of  the  steam  is  exactly  the 
same  as  the  temperature  of  the  water  from  which  it  is  formed,  namely, 
212°  F.  As  we  continue  to  add  heat,  more  and  more  of  the  water  is  evap- 
orated, until  finally  when  the  total  amount  of  heat  added  from  the  beginning 
of  the  experiment  is  1150.4  B.T.U. ,  the  last  bit  of  water  is  evaporated. 
The  volume  of  the  steam  formed  at  this  pressure  from  the  pound  of  water 
is  found  to  be  26.79  cubic  feet. 

64 


X"           To  Air  Pump             f\ 

Absolute 
Vacuum 

2116.3  Ib. 

1  Ib.  Water 

FIG.  17. — Ideal  apparatus  for  the 
investigation  of  the  properties 
of  vapors. 


ART.  84  THE   PHENOMENA  OF  VAPORIZATION  65 

From  the  time  that  the  water  reached  the  temperature  of  212°  until 
the  last  bit  of  it  evaporated,  the  temperature  remained  constant,  in  spite 
of  the  fact  that  970.4  B.T.U.  were  added  to  it  during  this  period.  A 
'part  of  the  energy  so  added  was  of  course  expended  in  lifting  the  weight 
upon  the  piston  a  distance  of  26.77  feet.  The  remainder  of  the  energy 
was  expended  in  separating  the  molecules  of  water  from  each  other 
against  the  forces  exerted  by  their  mutual  attractions.  The  first  quantity, 
which  is  56,700  foot  pounds,  or  72.8  B.T.U. ,  is  known  as  the  external 
work  of  evaporation,  while  the  second  quantity,  which  is  the  difference, 
or  879.6  B.T.U.,  is  known  as  the  internal  energy  of  evaporation.  Since 
the  whole  of  this  heat  added  during  the  evaporation  of  the  steam  produces 
no  rise  in  temperature,  but  is  transformed  into  some  other  form  of  energy, 
which  is  in  the  nature  of  potential  energy,  the  heat  so  transformed  is 
termed  latent  heat,  and  the  sum  of  the  internal  energy  and  the  external 
work  is  known  as  the  latent  heat  of  evaporation. 

83.  The  steam  contained  in  the  cylinder,  when  free  from   water,  is 
said  to  be  dry.     Since  it  is  at  the  same  temperature  as  the  water  from  which 
it  was  formed,  and  the  slightest  reduction  in  temperature  would  recon- 
dense  it  into  water,  it  is  also  said  to  be  saturated.     If  this  dry  and  saturated 
steam  be  heated  still  further,  we  will  find  that  its  temperature  begins 
to  rise,  and  that  it  takes  approximately  0.47  B.T.U.  per  pound  of  steam 
to  raise  its  temperature  one  degree.     As  more  and  more  heat  is  added, 
it  will  be  found  that  the  temperature  of  the  steam  continues  to  rise, 
but  that  the  rise  in  temperature  is  not  strictly  proportional  to  the  amount 
of  heat  added.     Careful  experiments  indicate  that  to  raise  its  temperature 
from  213°  to  313°  requires  46.9  B.T.U.,  to  raise  it  from  313°  to  413° 
requires  46.8  B.T.U.,  to  raise  it  from  413°  to  513°  requires  46.7  B.T.U. 

84.  Vaporization  at  Other  Pressures.     Had  we  heated  one  pound  of 
water  in  this   apparatus  under  a  different  pressure,  say    for    instance 
14,400  pounds  per  square  foot,  the  phenomena  observed  would  have  been 
of  exactly  the  same  kind. 

The  water  would  be  heated  to  a  temperature  of  327.8°  before  steam 
began  to  form;  298.3  B.T.U.  would  have  been  necessary  to  produce 
this  rise  in  temperature.  After  the  addition  of  888.0  more  B.T.U.,  the 
last  bit  of  water  would  evaporate  and  the  steam  formed  would  be  found 
to  occupy  a  volume  of  3.012  cubic  feet.  Any  further  addition  of  heat 
would  then  increase  the  temperature  of  the  steam.  To  raise  the  tem- 
perature from  327.8°  to  427.8°  would  require  54.5  B.T.U.  To  raise  it 
from  427.8°  to  527.8°  would  require  59.7  B.T.U.  To  raise  it  from  527.8° 
to  627.8°  would  require  58.4  B.T.U. 

85.  Temperature  of  Vaporization.     In  general,  from  such  an  exper- 
iment,  or   from   other   experiments   designed   to   investigate   the    same 
phenomena,  it  may  be  shown  that  the  phenomena  produced  by  the  addi- 


66  THE  THERMAL   PROPERTIES  OF  VAPORS  ART.  86 

tion  of  heat  to  one  pound  of  water  confined  under  a  constant  pressure  are 
invariably  as  follows:  When  water  is  confined  under  any  given  pressure, 
the  addition  of  heat  increases  its  temperature,  and  it  boils  when  the  tem- 
perature reaches  a  definite  value.  This  temperature  is  known  as  the 
temperature  of  vaporization  of  steam  of  the  given  pressure,  since  the  steam 
formed  has  the  same  temperature  as  the  water  from  which  it  is  formed. 
The  symbol  used  for  the  temperature  of  vaporization  is  engineering  work, 
(for  instance  in  steam  tables  and  thermodynamic  equations)  is  t,  and  it 
is  expressed,  in  engineering  work,  in  degrees  F.  The  symbol  used  in 
engineering  work  for  the  pressure  of  steam  is  p,  and  the  pressure  is 
expressed  in  pounds  per  square  inch  absolute. 

86.  Heat  of  the  Liquid.     The  amount  of  heat  required  to  raise  one 
pound  of  water  from  the  ice  point  to  any  given  temperature  of  vaporiza- 
tion,1 without  the  formation  of  steam,  is  a  definite  quantity.     This  quan- 
tity of  heat  is  known  as  the  heat  of  the  liquid.     The  symbol  used  for  the 
heat   of  the  liquid  in  engineering  work  is  h}2  and  it  is  expressed  in  B.T.U. 

87.  Vaporization.     Upon  the  further  addition  of  heat  to  water  having 
the  temperature  of  vaporization  corresponding  to  the  pressure  under  which 
it  is  confined,  it  is  transformed  into  steam  without  further  increase  in 
temperature,  so  long  as  any  water  remains  un transformed.     After  all 
the  water  is  transformed  into  steam,  any  further  addition  of  heat  increases 
the  temperature  of  the  steam. 

Steam  which  has  the  same  temperature  as  that  of  the  water  from 
which  it  was  formed  (i.e.  which  has  the  temperature  of  vaporization 
corresponding  to  its  pressure)  is  said  to  be  saturated,  since  any  reduction 
in  temperature  will  condense  some  of  it  into  water,  and  reduce  the  pressure. 
Steam  which  does  not  contain  any  water  suspended  in  it  in  the  form  of 
drops  or  mist  is  said  to  be  dry.  Steam  which  contains  no  suspended 
moisture,  and  yet  has  the  temperature  of  vaporization  corresponding 
to  its  pressure,  is  said  to  be  dry  and  saturated. 

88.  Specific   Volume  and  Density.     The  volume  of   1  pound  of   dry 
and  saturated  steam  at  any  given  pressure  is  a  definite  quantity.     This 
volume  is  known  as  the  specific  volume  of  steam  of   that   pressure    (or 
corresponding  temperature).     The  symbol  for  specific  volume  is  V,  and 
the  specific  volume  is  expressed  in  engineering  work  in  cubic  feet. 

The  weight  of  one  cubic  foot  of  dry  and  saturated  steam  of  any  pres- 

1  The    exact    amount    of    heat    required    varies    slightly  with   the    pressure  con- 
ditions.    The  water  may  be  heated  under  the  pressure  at  which  it  is  finally  vaporized, 
as  in  the  ideal  experiment  described  in  Art.  82.     It  may  be  heated  under  the  pressure 
produced    by  its  own  vapor,  which  grows  steadily  greater  as    the  temperature  rises. 
Or  it  may  be  heated  under  barometric  pressure,  until  its  temperature  corresponds  to 
this  pressure,  and  thereafter  be  heated  under  the  pressure  of  its  own  vapor.     The 
last  method  is  the  one  usually  assumed  to  be  employed. 

2  In  some  cases  the  symbol  q  is  used. 


ART.  89  LATENT  HEAT  67 

sure  is  termed  the  density  of  the  steam  at  that  pressure,  (or  corresponding 
temperature).  The  density  of  steam  is  the  reciprocal  of  its  specific 
volume  at  the  same  pressure,  and  is  therefore  a  definite  quantity  for  any 
given  pressure.  It  is  indicated  by  the  symbol  1/F,  and  is  expressed  in 
pounds  per  cubic  foot. 

89.  Latent    Heat.     The  quantity  of  heat  required  to  vaporize  com- 
pletely  1  pound  of   water  into  dry  and   saturated   steam  of  the  same 
temperature  as  the  water,  is  a  definite  quantity  for  any  particular  tem- 
perature.    This  quantity  of  heat  is  called  the  latent  heat  of  evaporation 
of  steam   of  the  given  temperature    (or   corresponding  pressure).     The 
symbol  for  the  latent  heat  of  evaporation  is  L1,  and  it  is  expressed  in 
engineering  work  in  B.T.U. 

90.  Total  Heat.      The  quantity  of    heat  required   to  raise    1    pound 
of  water  from  the  ice  point  to  any  temperature  of  vaporization  and  to 
evaporate  it  into  dry  and  saturated  steam  having  that  temperature,  is  a 
definite  quantity.     This  quantity  of  heat  is  called  the  total  heat  of  the 
steam  at  the  given  temperature  (or  corresponding  pressure) ,  and  is  expressed 
in  B.T.U.     The  symbol  used  in  engineering  work  for  the  total  heat  of  the 
steam  is  H. 

91.  External   Work.      The   work   done    by     1    pound   of    steam    in 
expanding  from  the  volume  occupied    by  1  pound  of  water  of  any  tem- 
perature to  the  specific  volume  of  dry  and  saturated  steam  of   the  same 
temperature,   against   the   pressure   corresponding   to   this   temperature, 
is  called  the  external  work  of  evaporation  of  steam  of    the    given    tem- 
perature (or  corresponding  pressure).     Since  both  the  change  in  volume 
and  the  pressure  are  definite  quantities  for  any  given  temperature,  the 
external  work  of  evaporation  is  also  a  definite  quantity  for  any  given 

144PF" 

temperature.     The  symbol  for  this  quantity  is ^ — ,  and  it  is  expressed 

J 

in  B.T.U. 

92.  Internal   Energy.     The    difference   between    the   latent    heat    of 
evaporation  and  the  external  work  of  evaporation  is  called  the  internal 
energy  of   evaporation.2     The  s}^mbol  for  the  internal  energy  of  evapora- 
tion of  steam  of  any  given  temperature  is  /  and  the  quantity  is  expressed 
in   B.T.U.     The   internal   energy   of  evaporation  plus  the  heat   of  the 
liquid  is  known  as  the  internal  energy  of  the  steam.     The  symbol  for  the 
internal  energy  of  the  steam  is  E}  and  this  quantity  is  also  expressed  in 
B.T.U. 

93.  Entropy  of  Steam.     The  integral  of  the  quantity  •=-  between  the 

1 

limits  of   32°  F.,  and  any  temperature  of  vaporization  is   known  as  the 
£• 

1  In  some  cases  the  symbol  r  is  used. 

2  The  term  " disgregational  energy"  is  also  used. 


68  THE  THERMAL  PROPERTIES  OF  VAPORS  ART.  94 

entropy  of  the  liquid  at  that  temperature  (or  corresponding  pressure). 
The  symbol  for  the  entropy  of  the  liquid  is  M.1  Entropy  is  an  abstract 
quantity. 

The  latent  heat  of  evaporation  of  1  pound  of  steam  divided  by  the 
absolute  temperature  of  the  steam  is  known  as  the  entropy  of  evaporation. 

The  symbol  for  entropy  of  evaporation  is  ™  The  sum  of  the  entro- 
pies of  the  liquid  and  of  evaporation  is  known  as  the  entropy  of  the 
steam  and  the  symbol  for  this  quantity  is  A^.2 

94.  Steam  Tables.  All  of  the  quantities  enumerated  above  are  of 
interest  and  of  practical  use  in  engineering  work.  They  are  known 
collectively  as  the  properties  of  steam,  and  a  table  giving  their  values 
for  steam  of  different  pressures  or  temperatures  is  known  as  a  table  of 
the  properties  of  steam.  Such  tables  were  first  accurately  computed  by 
the  French  scientist  Regnault,  who  devoted  some  years  to  a  study  of  the 
best  methods  of  determining  these  properties,  and  whose  work  was  of 
such  a  high  character  as  to  be  a  model  of  engineering  exactitude.  These 
properties  have  since  been  redetermined  by  many  other  scientists,  who- 
have  used  in  their  investigations  the  most  accurate  instruments  which 
it  was  possible  to  construct.  Since  in  most  cases  different  investigators 
have  used  different  methods  in  carrying  out  these  investigations,  their 
work  has  served  as  a  check  upon  that  of  each  other  and  also  upon  that 
of  Regnault,  so  that  the  properties  of  steam  over  a  considerable  range  of 
pressure  and  temperature  are  now  very  accurately  determined.  These 
properties  have  been  embodied  in  two  sets  of  tables  available  to  the 
English-speaking  engineer,  one  by  Marks  and  Davis,  and  the  other  by 
Peabody.  The  properties  quoted  in  this  book  are  invariably  from  the 
tables  of  Marks  and  Davis,  unless  otherwise  stated. 

96.  Experimental  Determination  of  the  Properties  of  Steam.  The  proper- 
ties of  dry  and  saturated  steam  of  a  given  temperature  which  are  determined  by 
direct  experiment,  are  the  pressure,  the  heat  of  the  liquid,  and  the  total  heat  of  the 
steam.  A  steam  table  usually  gives  us  the  properties  of  steam  for  each  degree  of 
temperature  from  32°  to  400°  F.  It  must  not  be  inferred,  however,  that  the  properties 
of  steam  have  been  determined  experimentally  for  every  degree  of  temperature  within 
this  range.  Like  other  physical  phenomena,  these  properties  are  interrelated  by 
certain  natural  laws,  and  therefore  their  relations  may  be  expressed  with  great 
accuracy  by  empirical  equations.  A  statement  of  the  method  by  which  these  proper- 
ties have  been  determined  experimentally  and  their  values  computed  for  steam 
tables,  will  be  of  interest. 

The  relation  between  the  pressure  and  the  temperature  of  saturated  steam  may  be 
determined  experimentally  by  simultaneously  measuring  the  temperature  and  the 
pressure  of  such  steam  by  suitable  instruments.  It  is  necessary,  of  course,  that 

1  The  letter  <j>  is  often  used.  2  The  letter  6  is  often  used. 


ART.  96  DETERMINATION  OF  THE   PROPERTIES  69 

these  instruments  be  accurate,  that  they  be  properly  calibrated,  and  that,  in  general, 
the  work  be  so  conducted  as  to  eliminate  errors.  After  determining  experimentally 
a  series  of  values  for  the  pressure  of  saturated  steam  of  different  temperatures,  it  is 
necessary  to  discover  an  equation  expressing  the  relationship.  Many  such  equations 
have  been  proposed,  the  most  accurate  of  which  is  that  of  Marks,  which  has  the 
following  form :  1 

log  p  =  10.515354  -  4873.71  T~l  -  0.00405096T  +  0.000001392964  71' 

where  p  is  the  pressure  of  the  steam  in  pounds  per  square  inch  and  T  is  the  absolute 
temperature  of  the  steam  in  Fahrenheit  degrees. 

The  heat  of  the  liquid  may  be  determined  by  measuring  the  quantity  of  electrical 
energy  used  in  heating  a  known  weight  of  water  from  the  ice-point  to  any  required 
temperature.  In  conducting  such  an  experiment,  it  is,  of  course,  necessary  to  take 
precautions  against  many  different  kinds  of  errors.  No  satisfactory  formula  for  the 
heat  of  the  liquid  has  yet  been  produced  except  the  one 

q  -  (*-32)  +  C, 

in  which  C  is  a  correction  determined  from  a  graphical  representation  of  the  results 
of  the  experimental  work. 

The  determination  of  the  total  heat  of  the  steam  is  the  most  difficult  part  of  all 
the  experimental  work  in  this  field.  The  principal  difficulty  lies  in  the  impossibility 
of  obtaining  absolutely  dry  and  saturated  steam.  However,  several  methods  have 
been  used  which  give  results  known  to  be  accurate  within  yio  of  1  per  cent  of  the 
total  value  of  the  quantity.  The  result  of  these  experiments  may  be  represented 
for  temperatures  above  212°  by  the  equation,2 

#  =  1150.3+0.3745(*-212)-0.000550(*--212)2. 

From  this  equation  and  from  graphical  representations  of  experimental  work  covering 
the  range  below  212°,  the  value  for  the  total  heat  of  saturated  steam  may  be  computed 
for  each  degree  of  temperature  within  the  range  which  a  steam  table  is  intended  to 
cover. 

96.  The  Computation  of  Properties  not  Directly  Observed.  All  other 
properties  of  steam  are  determined  from  the  pressure,  temperature  of  vaporization, 
heat  of  the  liquid,  and  total  heat  of  the  steam  by  means  of  the  thermodynamic  rela- 
tions of  these  four  quantities.  The  latent  heat  of  evaporation  is  obtained  by  sub- 
tracting the  heat  of  the  liquid  from  the  total  heat  of  the  steam.  The  entropy  of 

dh 

the  liquid  is  found  by  a  step-by-step  integration  of  the  quantity  — ,  and  the  entropy 

of  evaporation  by  dividing  the  latent  heat  of  evaporation  by  the  absolute  tempera- 
ture of  vaporization.  The  total  entropy  of  the  steam  is  the  sum  of  the  entropies 
of  the  liquid  and  of  evaporation. 

The  specific  volume  is  determined  in  the  following  manner :  Assume  that  1  pound  of 
steam  is  caused  to  perform  a  Carnot  cycle,  between  the  temperature  limits  T  andT  —  dT. 
The  Watt  diagram  of  this  cycle  is  shown  in  Fig.  18.  At  the  beginning  of  this  Carnot 
cycle  the  cylinder  of  the  Carnot  engine  will  contain  1  pound  of  water  at  a  tempera- 
ture T,  and  under  the  corresponding  pressure  P.  During  the  isothermal  expansion 
this  water  will  be  entirely  evaporated  by  adding  to  it  the  latent  heat  of  evaporation 

1See  the  Transactions  of  the  A.S.M.E.  for  1911. 

2  See  footnote  to  article  101  for  Davis'  method  of  determining  the  total  heat. 


70  THE   THERMAL  PROPERTIES   OF  VAPORS  ART.  97 

at  the  constant  temperature   T  and  the  corresponding  constant  pressure  P.     When 
the  pound  of  water  is  entirely  evaporated,  it  is  allowed  to  expand  adiabatically  until 

its  temperature  falls  by  the  infinitesimal 
amount  dT.  It  is  then  isothermally  com- 
pressed while  under  the  pressure  P—dP  and 
at  the  corresponding  temperature  T—dT. 
When  it  is  almost  entirely  condensed,  the 
condensation  is  stopped,  and  the  remainder 
of  the  compression  is  adiabatic,  raising  the 
-T—  temperature  of  the  mixture  of  steam  and 

p^  water   to   the  value  T,  and  condensing  the 

remaining     steam.       In     this     process,     the 
quantity  of    heat  imparted    to  the  water  is 
equal  to    the    latent    heat    of    evaporation. 
The    quantity  of   work    done    is,  of    course, 
~~  x        VdP,  where  V  is  the  increase  in  volume  of 
FIG.  18.— Oarnot  cycle  for  steam.  the    steam    (i  e  ?  the    difference    in    volume 

between  the    pound    of    dry  and  saturated 
steam  and  the  pound  of  water  under  the  given  pressure),  and  dP  is  the  change  in 

dT 
pressure.     The  efficiency  of  the  cycle  is,  of  course,  — .     Hence  we  may  write 

L~^L=vdp (i) 

Solving  this  for  V,  we  will  have 

V  =  ^X^| (2) 


If  we  plot  from  the  steam  tables  a  curve  showing  the  relation  of  the  temperature 
and  the  pressure  of  steam  (the  pressure  being  in  pounds  per  square  foot),  we  may 
at  any  point  in  this  curve  draw  a  tangent,  and  from  the  intercepts  we  may  determine 

dT 
the  value  of  the  expression  — .     By  means  of  this  value,  and  the  known  latent  heat 

of  evaporation  for  the  given  temperature,  we  may  compute  the  increase  in  volume  V, 
and  by  adding  to  this  the  original  volume  of  the  water,  we  obtained  the  volume  of 
the  steam  at  the  given  temperature  and  pressure.  After  obtaining  the  specific 
volume  for  a  number  of  temperatures,  we  may  construct  a  curve  or  derive  an  equation 
from  which  the  specific  volume  of  steam  of  any  temperature  may  be  determined. 
The  density  of  steam  is,  of  course,  the  reciprocal  of  the  specific  volume  of  the  steam. 

The  external  work  of  evaporation  is  found  by  multiplying  the  change  in  volume 
in  passing  from  the  condition  of  a  liquid  to  the  condition  of  dry  and  saturated  steam, 
by  the  pressure  of  the  steam  in  pounds  per  square  foot.  This  quantity  divided  is 
by  777.5  in  order  to  reduce  it  to  B.T.U.  The  internal  energy  of  evaporation  is  equal 
to  the  latent  heat  of  evaporation  minus  the  external  work  of  evaporation.  The 
internal  energy  of  the  steam  is  equal  to  the  internal  energy  of  evaporation  plus 
the  heat  of  the  liquid. 

97.  The  Properties  of  Other  Vapors.  The  phenomena  observed  when 
other  liquids  than  water  are  evaporated  into  their  vapors  are  exactly 
similar  to  the  phenomena  observed  in  the  case  of  water.  The  quantities 


ART.  97  PROBLEMS  71 

of  heat,  the  pressure,  the  temperatures,  the  specific  volume,  etc.,  will 
of  course  be  different  for  different  vapors,  but  the  methods  of  determining 
these  quantities  are  the  same  for  all  vapors.  In  the  case  of  such  vapors 
as  sulphur-dioxide,  ammonia  ether,  alcohol,  chloroform,  carbon  bisul- 
phide, carbon  tetrachloride,  and  aceton,  which  are  vapors  used  commer- 
cially in  refrigerating  machines  of  various  types,  the  properties  have  been 
determined  with  some  degree  of  accuracy  and  are  embodied  in  tables 
available  to  engineers. 

« 
PROBLEMS 

Find  from  a  steam  table  the  properties  of  steam  asked  for  in  the  following  prob- 
lems. The  answers  are  from  the  tables  of  Marks  and  Davis.  Other  answers  will 
usually  be  obtained  by  the  use  of  other  tables.  Interpolate  when  necessary. 

1.  What  is  the  temperature  of  vaporization  of  steam  at  pressures  of  1  Ib.  absolute? 
10  Ibs.  absolute,  and  100  Ibs.  gage?  Ans:     101.8°,  193.2°,  and  337.9°. 

2.  What  is  the  pressure  of  saturated  steam  at  temperatures  of  100°,  200°,  and  300°? 

Ans.     0.946,  11.52,  and  67.00  Ibs.  per  square  inch. 

3.  Find  the  heat  of  the  liquid  in  each  case  in  Problem  1. 

Ans.     69.8  and  308.8  B.T.U. 

4.  What  quantity  of  heat  is  required  to  raise  1  Ib.  of  water  from  the  ice-point  to 
the  several  temperatures  given  in  Problem  2?     Ans.     67.97,  167.9,  and  269.6  B.T.U. 

5.  What  is  the  volume  of  1  Ib.  of  dry  and  saturated  steam  at  the  pressures  given 
in  Problem  1?  Ans.     339.0,  38.38,  and  3.886  cu.ft. 

6.  What  is  the  density  of  dry  and  saturated  steam  at  the  temperatures  given  in 
Problem  2?  Ans.     0.008251,  0.02976,  and  0.1547  Ibs.  per  cu.ft. 

7.  Find  the  latent  heat  of  evaporation  of  steam  at  the  pressures  given  in  Problem 
1 .  Ans.     1034.6,  982.0,  and  880.0  B.T.U. 

8.  Find  the  total  heat  of  steam  at  the  temperatures  given  in  Problem  2. 

Ans.     1103.6,  1145.8,  and  1179.1  B.T.U. 

9.  Find  the  internal  energy  of  evaporation  of  1  Ib.  of  steam  at  the  three  pressures 
given  in  Problem  1.  Ans.     972.2,  910.9,  and  789.1  B.T.U. 

10.  Find  the  external  work  of  evaporation  at  the  temperatures  given  in  Problem  2. 

Ans.     61.5,  71.6,  and  79.8  B.T.U. 

11.  Find  the  entropy  of  the  liquid  at  the  pressures  given  in  Problem  1. 

Ans.     0.1327,0.2832,  and  0.4875. 

12.  Find  the  increase  in  entropy  of  1  Ib.  of  water  when  it  is  evaporated  into  steam 
at  the  temperatures  given  in  Problem  2.  Ans.     1.8506,  1.4824,  and  1.1972. 

13.  Find  the  total  entropy  of  1  Ib.  of  steam  at  the  pressures  given  in  Problem  1. 

Ans.     1.9754,  1.7874,  and  1.5909. 


CHAPTER  VI 
WET   AND   SUPERHEATED   VAPORS 

98.  Quality  of  a  Vapor.     When  a  vapor  contains  suspended  within 
it  in  the  form  of    fine  bubbles  or  drops  a  quantity  of  the  liquid  from 
which  it  was  formed,  the  vapor  is  said  to  be  wet.     The  vapor  and  the 
suspended  liquid  have  the  same  temperature  and  are  under  the  same 
pressure,  and  the   whole  mass  may  therefore  be  said  to  be  in  a  state  of 
thermodynamic  equilibrium,  since  the  division  of  the  particles  of  liquid 
is  so  fine  that  during  expansion  or  compression  the  whole  mass  will  not 
only  remain  in  thermal  equilibrium,  but  it  will  remain  homogeneous  in 
character.     The  proportion  which  the  dry  and  saturated  vapor  present 
bears  by  weight  to  the  whole  quantity  of  the  mixture,  is  termed  the  quality 
of  the  wet   vapor  and  is  usually  expressed  as  a  per  cent.     The  symbol 
for  the  quality  of  a  wet  vapor  is  q.1     One  pound  of  wet  vapor  will  there- 
fore consist  of  q  pounds  of  dry  and  saturated  vapor,  and  of  l—q  pounds 
of  liquid.    Thus  1  pound  of  steam  of  90  per  cent  quality  contains  9/io  of 
a  pound  of  dry  and  saturated  steam,  and  there  is  I/\Q  of  a  pound  of  water 
suspended  in  this  steam. 

If  a  wet  vapor  be  thermally  isolated,  its  quality  will  remain  constant 
provided  the  pressure  remains  unchanged,  but  on  account  of  the  greater 
density  of  the  particles  of  fluid,  they  will  tend  to  fall  to  the  bottom  of  the 
containing  vessel,  thus  separating  the  wet  vapor  into  two  portions,  one 
consisting  of  dry  and  saturated  vapor,  and  the  other  of  liquid.  This 
process  of  course  destroys  the  homogeneity  of  the  wet  vapor  by  separating 
it  into  two  thermodynamic  bodies.  Since,  however,  the  diameter  of  the 
particles  of  liquid  is  exceedingly  small,  the  rate  at  which  they  descend 
through  the  vapor  is  also  small,  and  this  action  goes  on  but  slowly.  Con- 
sequently, wet  vapors  when  in  motion,  do  not  change  their  quality  in 
any  sensible  degree  during  short  periods  of  time. 

99.  Properties  of  a  Wet  Vapor.     The  heat  of  the  liquid  of  a  wet  vapor 
is  the  same  as  the  heat  of  the  liquid  of  the  dry  and  saturated  vapor  of 
the  same  temperature  (or  pressure). 

The  latent  heat  of  evaporation  of  a  wet  vapor  is  equal  to  the  latent 
heat  of  evaporation  of  the  dry  and  saturated  vapor  of  the  same  tem- 

1  The  symbol  x  is  often  used  for  this  quantity. 

72 


ABT  99  PROPERTIES  OF  A  WET  VAPOR  73 

•     • 
perafrture  (or  pressure)  multiplied  by  the  quality  of  the  wet  vapor.     This 

may  be  expressed  by  the  formula 

Lw  =  qL, 

in  which  Lw  is  the  latent  heat  of  evaporation  of  the  wet  vapor,  L  is  the 
latent  heat  of  evaporation  of  the  dry  and  saturated  vapor,  and  q  is  the 
quality  of  the  wet  vapor. 

The  total  heat  of  a  wet  vapor  is  the  sum  of  the  heat  of  the  liquid  and 
the  latent  heat  of  evaporation.     This  may  be  expressed  by  the  equation 


in  which  Hw  is  the  total  heat  of  the  wet  vapor,  h  is  the  heat  of  the  liquid, 
and  q  and  L  are  as  in  the  preceding  paragraph. 

Unless  the  quality  of  a  wet  vapor  is  very  low,  the  volume  of  the 
liquid  which  it  contains  is  only  a  small  proportion  of  the  whole  volume. 
We  may  therefore  take  as  the  specific  volume  of  a  wet  vapor  the  product 
of  the  specific  volume  of  the  dry  and  saturated  vapor  at  the  same  tem- 
perature (or  pressure)  into  the  quality  of  the  wet  vapor.  This  neglects,  of 
course,  the  volume  of  the  liquid,  but  no  material  error  is  introduced, 
as  this  is  entirely  negligible.  We  may  then  write  for  the  specific  volume 
of  a  wet  vapor  the  formula 


in  which  Vw  is  the  specific  volume  of  the  wet  vapor,  q  is-  the  quality,  and 
V  is  the  specific  volume  of  the  dry  and  saturated  vapor  at  the  same 
temperature. 

The  density  of  a  wet  vapor  is  the  reciprocal  of  its  specific  volume  and 
is  therefore  equal  to  the  density  of  the  dry  and  saturated  vapor  at  the 
same  temperature  (or  pressure)  divided  by  the  quality  of  the  wet  vapor. 

The  external  work  of  evaporation  of  a  wet  vapor  is  equal  to  the 
external  work  of  evaporation  of  the  dry  and  saturated  vapor  at  the  same 
temperature  (or  pressure),  multiplied  by  the  quality  of  the  vapor. 

The  internal  energy  of  evaporation  of  a  wet  vapor  is  equal  to  the  internal 
energy  of  evaporation  of  the  dry  and  saturated  vapor  at  the  same  tem- 
perature (or  pressure)  multiplied  by  the  quality  of  the  vapor. 

The  entropy  of  the  liquid  is  the  same  in  the  case  of  a  wet  vapor  as 
in  the  case  of  the  dry  and  saturated  vapor  of  the  same  temperature 
(or  pressure). 

The  entropy  of  evaporation  of  a  wet  vapor  is  equal  to  the  entropy 
of  evaporation  of  the  dry  and  saturated  vapor  at  the  same  temperature 
(or  pressure)  multiplied  by  the  quality  of  the  vapor. 


74  WET  AND  SUPERHEATED  VAPORS  ART.  100 

The  total  entropy  of  a  wet  vapor  is  equal  to  the  sum  of  the  entropies 
of  the  liquid  and  of  evaporation  and  may  be  expressed  by  the  formula 


in  which  Nw  is  the  total  entropy  of  the  wet  vapor,  q  is  its  quality,  M 
is  the  entropy  of  the  liquid  of  the  dry  and  saturated  vapor,  and  ^  is 

the  entropy  of  evaporation  of  the  dry  and  saturated  vapor. 

The  above  properties,  when  determined  by  the  methods  given,  will 
of  course  be  for  1  pound  of  wet  vapor.  The  properties  of  the  dry  and 
saturated  vapor,  in  the  case  of  steam  or  other  vapors  used  in  thermody- 
namic  machinery,  may  be  taken  from  tables.  If  the  quality  of  the  wet 
vapor  is  unknown,  but  its  temperatures  or  pressure,  and  its  total  heat 
or  total  entropy,  or  density  or  specific  volume,  or  its  latent  heat  or 
entropy  of  evaporation  is  known,  its  quality,  and  from  this  its  other 
properties,  may  be  computed  from  the  equations  or  by  the  methods 
developed  in  the  preceding  paragraphs. 

100.  Superheated  Vapors.     When  a  vapor  has  a  higher  temperature 
than    the    temperature  of    vaporization    corresponding   to    its  pressure, 
it  is  said  to  be  superheated.     The  state  of  a  superheated  vapor  is  defined 
in  practice  by  giving  either  its  temperature  and  pressure  or  by  giving  its 
pressure  and  the  amount  of    superheat.     The  amount    of    superheat  is 
obtained  by  subtracting  from  the  observed  or  computed  temperature  of 
the  superheated,  vapor   the  temperature  of  vaporization    corresponding 
to  the  observed  or  computed  pressure  of  the  vapor. 

101.  Properties  of  a  Superheated  Vapor.    The  latent  heat  of  evapora- 
tion, the  temperature  of  vaporization,  the  entropy  of  the  liquid,  the 
entropy  of  evaporation,  and  the  external  and  internal  energy  of  evapora- 
tion are  the  same  for  a  superheated  vapor  as  for  a  dry  and  saturated 
vapor  when  it  is  of  the  same  pressure  as  the  superheated  vapor. 

The  heat  of  superheat  of  a  vapor  is  the  quantity  of  heat  which  must 
be  imparted  to  1  pound  of  it  in  raising  it  from  the  temperature  of  vaporiza- 
tion to  its  actual  temperature,  at  the  pressure  of  vaporization.  This  is 
equal  to  the  amount  of  superheat  multiplied  by  the  mean  specific  heat 
of  the  vapor  at  constant  pressure,  for  the  given  conditions.  It  may  be 
noted  that  the  specific  heat  of  a  vapor  at  constant  pressure  varies  both 
with  the  temperature  and  with  the  pressure,  so  that  its  mean  value, 
for  the  particular  range  of  temperature  and  pressure  for  which  the  com- 
putation is  made,  should  be  employed.  The  specific  heat  of  superheated 
steam  has  been  determined  with  considerable  accuracy  by  several  observers. 
Thomas's  method  consists  in  electrically  heating  steam  already  slightly 


ART.  101  PROPERTIES   OF  A  SUPERHEATED   VAPOR  75 

superheated,  and  measuring  the  energy  required,  the  weight  of  steam 
superheated,  and  the  rise  in  temperature. 

The  total  heat  of  a  superheated  vapor  is  equal  to  the  total  heat  of  the 
dry  and  saturated  vapor  at  the  same  pressure  plus  the  heat  of  superheat. 
This  may  be  expressed  by  the  formula  1 

H8  =  H  +  Cp(ts-t] 

in  which  H8  is  the  total  heat  of  the  superheated  vapor,  H  is  the  total  heat 
of  the  dry  and  saturated  vapor  at  the  same  pressure,  ts  is  the  temperature 
of  the  superheated  vapor,  t  is  the  temperature  of  vaporization  correspond- 
ing to  its  pressure,  and  Cp  is  the  mean  specific  heat  of  the  superheated 
vapor  at  constant  pressure  for  the  pressure  and  range  of  temperature 
for  which  the  computation  is  made. 

When  the  amount  of  superheat  is  not  great,  the  specific  volume  of  a 
superheated  vapor  may  be  obtained  from  the  equation 

V  T 

V  —         * 

y  8   -         rp      } 

in  which  V  is  the  specific  volume  of  dry  and  saturated  vapor  of  the  same 
pressure,  T  is  the  absolute  temperature  of  vaporization  corresponding 
to  this  pressure,  and  T8  is  the  actual  temperature  of  the  vapor.  In  case 
the  superheat  is  great,  the  vapor  becomes  more  like  a  perfect  gas  in  its 
behavior  and  its  specific  volume  may  be  found  from  the  characteristic 
equation  of  gases,  or  better,  by  means  of  an  empirical  equation  derived 
from  a  knowledge  of  its  actual  behavior  at  different  temperatures  and 
pressures.  The  density  of  a  superheated  vapor  is  the  reciprocal  of  its 
specific  volume. 

The  entropy  of  a  superheated  vapor  is  found  by  adding  to  the  entropy 
of  the  dry  and  saturated  vapor  of  the  same  pressure  the  quantity  obtained 
by  a  step-by-step  integration  of  the  heat  additions  necessary  to  superheat 
the  vapor,  each  divided  by  the  absolute  temperature  at  which  they  occurred. 

1  When  superheated  steam  flows  through  a  porous  plug  (a  process  called  throttling), 
it  neither  gains  nor  loses  heat.  Consequently  we  mpy  write  the  formula 


in  which  the  right-hand  member  is  the  total  heat  before  throttling  and  the  left-hand 
members  the  total  heat  after  throttling.  In  each  member  the  first  term  will  usually 
1x3  large  as  compared  with  the  second,  and  an  error  in  the  determination  of  Cp  will 
therefore  have  a  comparatively  small  effect  upon  the  answer  when  we  solve  for  H' 
or  H".  Consequently,  if  the  total  heat  of  dry  and  saturated  steam  be  determined 
for  some  one  pressure,  from  a  series  of  throttling  experiments,  the  total  heats  at  other 
pressures  may  be  determined  with  great  accuracy.  This  method  is  due  to  Davis. 


76  WET  AND   SUPERHEATED   VAPORS  ART.  102 

If  the  specific  heat  of  superheat  of  the  vapor  be  assumed  to  be  constant, 
this  quantity  may  be  expressed  by  the  equation, 

N.  =  N  +  Cp  loge  £, 

in  which  N8  is  the  total  entropy  of  the  superheated  vapor,  N  is  the  total 
entropy  of  dry  and  saturated  vapor  of  the  same  pressure  as  the  super- 
heated vapor,  Cp  is  the  specific  heat  of  the  superheated  vapor  at  constant 
pressure,  Ts  is  the  absolute  temperature  of  the  superheated  vapor,  and 
T  is  the  absolute  temperature  of  vaporization  corresponding  to  the 
pressure  of  the  superheated  vapor.  In  practical  work,  the  entropy  of 
superheated  steam  as  well  as  the  values  of  the  other  properties  are  usually 
obtained  from  a  table. 

102.  The  Relation  between  Vapors  and  Gases.     At  this  point,  it  is 
proper  to  point  out  the  relations  existing  between  vapors  and  gases. 
It  has  already  been  stated  that  when  a  gas  is  sufficiently  cooled  and  com- 
pressed, it  will  condense  into  a  liquid.     During  the  process  of  cooling, 
it  is  reduced  from  a  sensibly  perfect  gas,  first  to  the  condition  of  a  highly 
superheated  vapor,  then  to  the  condition  of  a  slightly  superheated  vapor, 
then  to  the  condition  of  a  wet  vapor,  and  finally  it  is  entirely  transformed 
into  a  liquid.     There  is  no  definite  line  of  demarcation  which  separates 
any  one  of  these  states  from  the  next.     We  may  therefore  regard  a  gas 
as  being  in  the  condition  of  a  highly  superheated  vapor  even  though  the 
gas  be  sensibly  perfect. 

103.  The  Critical  State.      Experiment  shows  that  when  an  attempt 
is  made  to  liquefy  any  of   the  permanent  gases  by  the  application  of 
pressure,  that  the  attempt  will  fail  unless  the  temperature  of  the  gas  is 
below   a   certain   definite   value.     This    temperature    is    known   as   the 
critical  temperature  of  the  gas.       Experiment  has  also  shown  that  the 
latent  heat  of  evaporation  of  a  liquid  diminishes  as  the  temperature  and 
pressure  increases,  and  that  in  the  case  of  some  liquids  it  is  reduced  to 
zero  at  the  critical  temperature.     If  a  liquid  is  heated  to  the  temperature 
at  which  its  latent  heat  of  evaporation  becomes  zero,  it  will,  obviously, 
be  vaporized  without  further  addition  of  heat,  and  at  any  higher  temper- 
ature the  substance  can  exist  only  as  a  vapor.     Consequently,  the  critical 
temperature  of  a  substance  may  be  defined  as  that  temperature  at  which 
the  latent  heat  of  evaporation  of  its  liquid  becomes  zero.     The  pressure 
of  a  saturated  vapor  at  the  critical  temperature  is  known  as  the  critical 
pressure  of  the  substance.     This  is,  of  course,  the  pressure  which  is  required 
in  order  to  liquefy  the  vapor  when  it  has  the  critical  temperature.     The 
specific  volume  of   a  vapor  at  the  critical  temperature  and  pressure  is 
termed  the  critical  volume.      The  state  of  the  vapor  is  termed  the  critical 
state. 


ART.  104  THE   PHENOMENA   OF   FUSION  77 

104.  The  Phenomena  of  Fusion.     It  is  a  matter  of  experience  that  when 
a  liquid  is  cooled,  it  will  finally  be  transformed  into  a  solid  at  some  definite 
temperature  which  is  known  as  the  freezing  point  of  the  liquid,  and   also 
as  the  melting  point,  or  temperature  of  fusion  of  the  solid  into  which  it  is 
transformed.     Some    complex    organic    substances    and    some    mixtures 
of  simple  substances  do  not  have  a  definite  freezing-point,  but  all  elemen- 
tary substances  do,  as  do  also  almost  all  simple  compounds.     In  order 
to  transform  the  liquid  into  a  solid,  it  is  necessary  to  abstract  heat  from 
it  at  constant  temperature.     In  order  to  retransform  the  solid  into  a 
liquid,  it  is  necessary  to  add  to  this  the  same  quantity  of  heat,  at  the  same 
constant  temperature.     This  quantity  of  heat  is  known  as  the    latent 
heat  of  fusion.     The   melting-point   of   any   substance   varies  somewhat 
with  the  pressure,  but  the  range  is  usually  very  narrow. 

105.  Sublimation.     If  the  pressure  of  vaporization  of  a  liquid  at  the 
melting-point  of  the  solid  from  which  it  is  formed  is  greater  than  atmos- 
pheric pressure,  the  solid  cannot  be  melted  in  an  open  vessel,  but  will 
sublime  at  atmospheric  pressure.     A  substance  sublimes  when  its  vapor 
is  formed  directly  from  its  solid  form  by  the  addition  of  heat.      When 
the  vapor  so  formed  is  condensed,  it  will  condense  in  the  form  of  a  solid. 

It  is  evident  that  a  solid  substance  can  be  melted  only  in  the  presence 
of  its  own  vapor,  and  the  pressure  of  the  vapor  must  be  equal  to  the 
saturation  pressure  at  the  temperature  of  fusion,  for,  if  the  vapor  pressure 
be  less  than  the  saturation  pressure,  the  liquid  will  be  transformed  into 
vapor  the  instant  the  solid  melts.  Hence  the  phenomena  of  sublimation. 
The  pressure  of  other  vapors  and  gases  present  has  no  effect  in  preventing 
sublimation,  except  as  the  presence  of  such  gases  serves  to  prevent  the 
free  escape  of  the  vapor  which  is  being  sublimed. 

An  inspection  of  a  steam  table  will  show  that,  when  the  pressure  of 
the  water  vapor  present  in  the  air  is  less  than  0.0866  pounds  per  square 
inch,  ice  will  sublime,  since  as  fast  as  the  ice  is  melted,  the  water  formed 
will  instantly  disappear  as  vapor,  the  vapor  pressure  of  water  at  the 
melting-point  of  ice  being  0.0866  pounds  per  square  inch.  In  order  to 
obtain  water  from  ice  it  is  therefore  necessary  to  melt  the  ice  in  an  atmos- 
phere where  the  pressure  of  the  water  vapor  is  greater  than  the  value  given. 
Carbon  is  an  example  of  a  substance  which  cannot  be  liquefied  except 
at  very  high  pressures,  and  since  the  temperature  at  which  carbon  would 
melt  is  exceedingly  high,  it  is  impossible,  by  any  means,  to  obtain  liquid 
carbon.  Could  we  do  so,  it  would  in  all  probability  crystallize  in  the 
form  of  the  diamond,  on  solidifying,  just  as  ice  crystals  are  formed  from 
water  at  suitable  pressures  (i.e.,  at  a  pressure  greater  than  0.0866  pounds 
per  square  inch). 

Most  solids  sublime  to  a  noticeable  extent  at  temperatures  approach- 
ing their  melting-point;  carbon,  for  instance,  sublimes  from  the  filament 


78  WET   AND   SUPERHEATED   VAPORS  AKT.  105 

within  the  bulb  of  the  incandescent  lamp,  and  is  deposited  in  the  form 
of  a  thin  film  on  the  interior  of  the  glass.  Ice  and  snow  also  sublime  at 
temperatures  far  below  freezing.  Even  a  cold  wind  will  cause  the  rapid 
disappearance  of  a  snowbank  provided  the  air  is  dry  (i.e.,  the  pressure 
of  the  water  vapor  present  is  very  low) .  While  we  cannot  state  positively, 
it  is  quite  possible  that  all  solid  substances  are  continually  subliming  at  a 
very  slow  rate,  and  would  in  the  course  of  centuries  lose  appreciably 
in  weight.  We  know  that  this  is  true  in  the  case  of  certain  substances, 
which  gradually  disappear  at  temperatures  below  their  melting-point 
unless  confined  within  an  air-tight  space. 

106.  Isothermal  Expansion  of  Vapors.     When  a  vapor  is  caused  to 
expand  without  the  addition  of  heat,  its  temperature  falls.     Consequently, 
if  a  vapor  is  caused  to  expand  isothermally,  heat  must  be  added  to  it. 
If  the  vapor  be  wet,  this  heat  will  vaporize  the  moisture  present  as  the 
expansion  progresses,  and  so  long  as  any  moisture  is  present,  the  expansion 
will  be  isobaric  as  well  as  isothermal,  for  the  least  fall  in  pressure  will 
lower  the  temperature  of  vaporization  of  the  liquid,  and  cause  it  to  evap- 
orate at  such  a  rate  as  to  restore  the  pressure  to  that  corresponding  to  the 
temperature.     For  instance,  if  a  mixture  of  steam  and  water  be  confined 
at  constant  pressure  and  heat  be  supplied,  the  water  will  be  evaporated, 
and  the  volume  will  increase,  but  the  pressure  and  temperature  of  the 
mass    will    both   remain    constant.     The    pressure-volume    curve    which 
represents  the  isothermal  expansion  of  a  mass  of  wet  vapor  is,  therefore, 
a  horizontal  line.     The  work  done  during  such  isothermal  expansion  is, 
of  course,  equal  to  the  product  of  the  pressure  (in  pounds  per  square  foot) 
into  the  change  in  volume  (in  cubic  feet) ,  and  is  also  equal  to  the  external 
work  of  evaporation  of  the  quantity  of  liquid  evaporated  during  isothermal 
expansion.     The  quantity  of  liquid  so  evaporated  may  be  deduced  from 
the  specific  volume  of  the  vapor  and  the  observed  or  computed  change 
in  volume  during  the  expansion. 

If  the  isothermal  expansion  of  a  vapor  be  continued  after  it  has  become 
dry,  the  vapor  will  become  superheated,  since  the  pressure  will  fall  off 
and  the  temperature  will  remain  constant.  As  the  expansion  progresses, 
the  amount  of  superheat  becomes  greater  and  greater  as  the  pressure 
becomes  lower,  and  the  condition  of  the  vapor  approaches  more  and  more 
that  of  a  perfect  gas.  The  pressure-volume  curve  for  the  isothermal 
expansion  of  a  superheated  vapor  resembles  that  of  a  gas  and  may  be 
very  nearly  represented  by  a  rectangular  hyperbola.  This  method  of 
vaporous  expansion  is  not,  however,  of  great  importance  in  the  theory 
of  thermodynamic  machinery,  since  it  is  never  met  with  in  practice. 

107.  Expansion  without  Change  of  Quality.      A  mass  of  vapor  may 
be  caused  to  expand,  and  to  remain  in  the  dry  and  saturated  condition 
throughout  the  expansion,  by  the  addition  or  abstraction  of  heat  at  the 


AET.  108  ADIABATIC   EXPANSION  79 

proper  rate.  The  pressure-volume  curve  of  a  mass  of  steam,  when  it 
expands  under  such  circumstances,  is  known  as  the  line  of  constant  steam 
weight,  and  it  may  be  plotted,  point  by  point,  from  a  steam  table,  by 
making  the  volume  of  the  mass  of  vapor  proportional  to  the^  specific 
volume  of  dry  and  saturated  steam  for  each  of  the  several  pressures  for 
which  the  points  are  plotted.  The  plotting  of  this  curve  is  a  matter  of 
importance  in  the  analysis  of  steam-engine  and  steam-turbine  tests.  If 
a  vapor  which  condenses  by  adiabatic  expansion  be  caused  to  expand 
slowly  within  a  conducting  cylinder  while  the  walls  of  the  cylinder  are 
maintained  at  a  temperature  slightly  higher  than  the  initial  temperature 
of  the  vapor,  it  will  expand  in  this  manner,  since  a  wet  vapor  quickly 
takes  up  heat,  while  a  dry  one  does  not.  As  soon  as  any  of  the  vapor 
is  condensed  by  expansion,  the  liquid  formed  is  immediately  re-evaporated 
by  the  heat  from  the  walls  of  the  cylinder.  In  certain  kinds  of  engineer- 
ing apparatus  it  is  found  that  this  method  of  vaporous  expansion  is  quite 
closely  approximated. 

108.  Adiabatic  Expansion.  A  vapor  is  caused  to  expand  adiabatically 
when  it  is  confined  within  a  non-conducting  cylinder  or  when  it  is  allowed 
'to  flow  through  a  properly  formed  nozzle.  The  successive  states  of  a 
mass  of  vapor  undergoing  adiabatic  expansion  all  have  the  same  entropy. 
In  the  case  of  a  vapor,  we  cannot  write  a  rational  equation  connecting 
the  pressure  and  volume,  or  temperature  and  volume,  of  the  mass  of 
expanding  fluid,  as  we  can  in  the  case  of  a  gas.  It  is  therefore  impossible 
to  compute  directly  the  exact  effects  of  adiabatic  expansion  upon  the 
temperature,  pressure,  and  quality  of  the  vapor,  although  numerous 
empirical  equations  have  been  given  by  different  investigators  which 
give  results  which  are  approximately  correct  for  limited  ranges  of  expan- 
sion. However,  by  means  of  the  relations  between  the  total  entropy 
of  a  vapor  and  its  other  properties,  we  may  compute  for  any  particular 
case,  the  properties  of  the  vapor  when  its  initial  temperature  or  pressure 
and  quality  and  its  final  temperature  are  known.  Thus  if  vapor  of 
known  properties  (i.e.,  temperature  or  pressure,  quality  and  total  entropy), 
l)e  caused  to  expand  adiabatically  to  some  other  temperature  or  pressure, 
its  total  entropy  at  the  new  state  will  be  the  same  as  it  was  initially. 
From  the  known  total  entropy  and  temperature  or  pressure  at  the  new 
state,  we  may  compute  the  entropy  of  vaporization,  the  quality  of  the 
vapor,  and  any  other  properties  which  are  desired.  For  instance,  if 
steam  of  350°  temperature  and  98  per  cent  quality  be  caused  to  expand 
adiabatically  to  a  temperature  of  110°,  we  may  find  its  properties  at  the 
lower  temperature  in  the  following  manner:  The  entropy  of  the  liquid 
at  350°  is  0.5032.  The  entropy  of  evaporation  of  the  wet  steam  is  0.98  X 
1.0748=1.0533.  The  total  entropy  of  the  steam  at  110°  will,  since  the 
expansion  is  adiabatic,  be  the  same  as  it  was  at  350°,  namely,  .5032+ 


80  WET  AND  SUPERHEATED   VAPORS  ART.  109 

1.0533  =  1.5565.  The  entropy  of  evaporation  will  be  found  by  subtracting 
from  the  total  entropy  of  the  steam  the  entropy  of  the  liquid  at  110°, 
which  is  0.1471,  giving  for  the  entropy  of  evaporation  of  the  wet  steam 
1.4094.  The  quality  of  the  steam  may  now  be  found  by  dividing  the 
entropy  of  evaporation  of  the  wet  steam  by  that  of  dry  and  saturated 
steam.  In  this  case  the  quality  will  be 

U)°94     77.9  per  cent. 


From  this  quality  the  other  properties  of  the  wet  steam  may  be  determined. 
109.  Effect  of  Adiabatic  Expansion  on  the  Properties  of  a  Vapor. 

When  the  total  entropy  of  dry  and  saturated  vapor  decreases  as  the  tem- 
perature of  vaporization  increases,  the  vapor  will  be  partly  condensed  as 
a  result  of  adiabatic  expansion  unless  it  is  highly  superheated  or  very 
wet  at  the  beginning  of  the  expansion.  Most  vapors  are  of  this  character, 
steam  being  a  good  example  of  the  type.  When  steam  expands  adia- 
batically,  a  portion  of  it  will  condense  so  long  as  the  initial  quality  of  the 
steam  is  greater  than  about  50  per  cent.  On  the  other  hand,  the  prop- 
erties of  certain  kinds  of  vapors  are  such  that  the  entropy  of  the  dry 
and  saturated  vapor  increases  with  the  temperature  of  vaporization. 
Such  vapors  superheat  when  they  expand  adiabatically.  Ether  is  an 
example  of  such  a  vapor.  If  it  be  initially  dry  and  saturated  and  be  caused 
to  expand  adiabatically,  it  will  be  superheated,  while  if  it  is  initially 
wet,  it  will  become  dryer  as  a  result  of  the  expansion.  Vapors  which 
condense  by  adiabatic  expansion  are  dried  or  superheated  by  adiabatic 
compression,  and  those  which  are  superheated  or  dried  by  expansion 
are  condensed  by  adiabatic  compression.  Thus  steam  when  very  wet  is 
condensed,  and  when  nearly  dry  is  dried  by  adiabatic  compression. 

We  may  determine  the  adiabatic  expansion  line  of  a  vapor  point  by 
point,  by  determining  its  specific  volume  at  several  pressures  by  the 
principles  outlined  in  Art.  108.  In  the  same  way  we  may  determine  the 
total  heat,  or  any  other  desired  property,  of  an  expanding  vapor  for 
different  temperatures  (or  pressures).  If  desirable,  we  may  derive  an 
empirical  equation  which  will  give  the  relation  between  the  property 
desired  and  the  temperature  or  pressure  of  the  expanding  vapor.  The 
design  of  turbine  nozzles  and  of  other  forms  of  steam  machinery  may  be 
greatly  facilitated  by  employing,  in  such  computations,  a  table  or  diagram 
which  gives  the  relations  between  the  temperature,  quality,  entropy, 
specific  volume  and  total  heat  of  a  vapor.  Peabody's  temperature- 
entropy  table  is  an  example,  giving  the  relation  of  the  quality,  total 
heat,  and  specific  volume  of  steam  to  its  temperature  and  entropy. 
Mollier's  diagram,  also  much  used  for  this  work,  gives  the  relations  of  the 


ART.  110 


STEAM   CALORIMETERS 


81 


quality  or  superheat,  and  the  pressure  of  steam,  to  its  total  heat  and 
entropy. 

110.  Work  of  Adiabatic  Expansion.     The  quantity  of  work  done  by 
a  mass  of  vapor  during  adiabatic  expansion  will  depend  upon  the  mass 
and  the  initial  quality  or  superheat  of   the  vapor,  and  upon  the  tem- 
perature or  pressure  limits  of  the  expansion.     It  will    be   equal  to  the 
difference    between   the    initial  and  final    internal  energy  of  the  vapor. 
For  a  further  development  of  the  theory  of  adiabatic  expansion  of  vapors, 
as  applied  in  practice  in   the  design  of  steam  turbines,  see  Arts.  201 
and  202. 

111.  Determination  of  the  Quality  of  a  Wet  Vapor.     In  practice,  all 
vapors  which  are  not  superheated  are  wet,  since  it  is  impossible  by  any 
means  at  our  command  to  obtain  a  vapor  which  is  exactly  dry  and  satu- 
rated, just  as  it  is  impossible  to  obtain 

two  points  which  are  exactly  a  given 
distance  apart.  Engineering  investi- 
gations often  therefore  involve  the 
determination  of  the  quality  or  super- 
heat of  a  vapor.  It  is  not  difficult  to 
measure  simultaneously  the  tempera- 
ture and  pressure  of  a  superheated 
vapor  and  thereby  determine  the 
superheat,  but  it  is  necessary  to  resort 
to  indirect  methods  in  order  to  deter- 
mine the  quality  of  a  wet  vapor.  The 
vapor  whose  quality  engineers  are 
most  often  obliged  to  determine  is 
steam.  An  instrument  for  determin- 
ing the  quality  of  steam  is  termed  a 
steam  calorimeter,  and  several  types  of 
such  instruments  are  in  use. 

112.  The   Throttling   Calorimeter. 
When  the  steam  which  is  being  tested 
contains   less   than  3    or  4  per   cent 
of    moisture,    and    the     pressure    is 

sufficiently  high,  it  is  usual  to  employ  a  type  of  calorimeter  originally 
devised  by  Professor  Peabody,  which  is  known  as  a  throttling  calorimeter, 
and  is  shown  in  Fig.  19.  The  essential  parts  consist  of  a  chamber  A, 
usually  made  of  pipe  fittings,  a  valve  B,  which  is  interposed  between  the 
chamber  and  the  source  of  steam,  and  a  thermometer  C,  which  is  inserted 
in  a  thermometer  well  D  near  the  center  of  the  chamber.  The  steam 
to  be  tested  is  taken  from  pipe  P  in  which  it  is  flowing  and  admitted  to 
the  chamber  through  the  valve,  which  is  kept  nearly  closed,  so  that  the 


a  —  Hair  Felt 


FIG.  19.— The  Peabody  throttling 
calorimeter. 


82  WET   AND   SUPERHEATED   VAPORS  ART.  113 

pressure  of  the  steam  in  the  chamber  is  about  that  of  the  atmosphere. 
The  pressure  of  the  steam  in  the  pipe  P  must  be  known.  The  total  heat 
per  pound  is  then  given  in  the  formula, 


(1) 


in  which  Hw  is  the  total  heat  per  pound  of  the  wet  steam  in  the  pipe  P, 
q  is  the  quality  of  the  steam  in  the  pipe,  LI  is  the  latent  heat  of  evaporation 
of  dry  and  saturated  steam  having  the  pressure  of  the  steam  in  the  pipe 
P}  and  hi  is  the  heat  of  the  liquid  at  the  pressure  of  the  steam  in  the  pipe. 
After  passing  through  the  valve  the  total  heat  of  the  steam  will  be  unal- 
tered, but  since  the  total  heat  of  dry  and  saturated  steam  as  atmospheric 
pressure  is  less  (in  case  q  is  sufficiently  large)  than  the  total  heat  Hw  of 
the  wet  steam,  the  steam  in  chamber  A  will  be  superheated,  and  the 
amount  of  its  superheat  may  be  determined  by  means  of  the  thermometer. 
The  total  heat  of  the  superheated  steam  in  A  will  be  given  by  the  formula, 

ta),  .........     (2) 


in  which  Ha  is  the  total  heat  of  dry  and  saturated  steam  at  atmospheric 
pressure,  t  is  the  F.  temperature  registered  by  the  thermometer,  ta  is  the 
saturation  temperature  of  steam  at  atmospheric  pressure,  and  .47  is  the 
specific  heat  of  superheated  steam  at  atmospheric  pressure.  Equating 
1  and  2  we  will  have 

9Li+/n  =  #a-K47(*-*ff)  .......     (3) 

Solving  3  for  q  we  will  have, 

fq) 

~     ........         VV 


113.  Errors  of  the  Throttling  Calorimeter.  The  results  given  by  the 
throttling  calorimeter  are  affected  by  the  following  sources  of  error:  First, 
loss  of  heat  by  radiation,  which  makes  the  total  heat  of  the  steam  in  the 
chamber  A  less  than  the  total  heat  of  the  steam  in  the  pipe  and  reduces 
the  apparent  quality  of  the  steam;  second,  back  pressure  in  the  chamber 
A  which  increases  the  temperature  registered  by  the  thermometer  and 
the  apparent  superheat  in  the  chamber  A  ;  third,  the  temperature  of  the 
blast  of  steam  issuing  from  the  valve  is  less  (since  part  of  its  total  heat 
is  in  the  form  of  kinetic  energy)  than  that  of  the  steam  in  the  chamber  A 
(where  the  kinetic  energy  of  the  blast  has  been  retransformed  into  heat), 
hence  if  this  blast  of  steam  strikes  the  thermometer  well,  the  thermometer 
reading  will  be  lower  than  it  should  be;  fourth,  the  sample  of  steam  taken 
from  the  pipe  may  contain  a  greater  or  less  proportion  of  water  than  the 


ART,  113         ERRORS   OF  THE   THROTTLING  CALORIMETER 


S3 


steam  flowing  in  the  pipe.  The  first  source  of  error  may  be  obviated 
by  clothing  the  calorimeter  in  some  non-conducting  material  or  by  arrang- 
ing it  so  that  the  chamber  A  is  sur- 
rounded by  a  steam  jacket,  as  is 
done  in  the  New  Hampshire  calori- 
meter shown  in  Fig.  20.  The  second 
source  of  error  may  be  eliminaled 
by  obtaining  the  exact  pressure  of 
the  steam  in  the  calorimeter  by 
means  of  a  pressure  gage  attached 
to  the  chamber  A.  It  is  usually 
more  convenient  and  quite  as  satis- 
factory to  allow  an  ample  opening 
for  the  escape  of  steam,  so  that  the 
pressure  in  the  calorimeter  shall  be 
only  a  small  fraction  of  a  pound 
greater  than  the  pressure  of  the 
atmosphere.  The  third  source  of 
error  may  be  eliminated  by  so- 
designing  the  calorimeter  that  the 
blast  of  steam  from  the  reducing 
valve  does  not  strike  upon  the  walls 
of  the  thermometer  well.  The  fourth 
source  of  error  is  the  most  difficult 
of  all  to  eliminate.  Steam  rising 

through  a  vertical  pipe  is  of  practically  uniform  quality,  hence  a  sample 
taken  from  such  a  pipe  will  represent  accurately  the  quality  of  the  steam. 

When  steam  flows  through  a 
horizontal  pipe  a  quantity  of 
water  flows  along  the  bottom 
of  the  pipe  and  the  lower 
strata  are  wetter  than  the 
upper  ones.  When  a  sample 
of  steam  is  taken  from  a  hori- 
zontal pipe  through  an  opening 
distant  45°  from  the  bottom 
of  the  pipe,  as  shown  in  Fig. 
21,  it  will  represent  the  aver- 
age quality  of  the  steam  in 
the  pipe  with  considerable 
accuracy.  A  sample  of  steam 
from  a  pipe  in  which  the 
may  be  taken  by  introducing  into  the  pipe 


FIG.  20. — New  Hampshire  throttling 
calorimeter. 


FIG.  21, 


To  C  alorimeter 
-Sampling  pipe  for  a  horizontal  steam 
pipe. 


steam  is  flowing  downward 


84 


WET  AND  SUPERHEATED  VAPORS 


ART.  114 


WWW 


To  Calorimeter 


FIG.  22. — Sampling  pipe  for 
a  vertical  steam  pipe. 


a  small  pipe  in  which  are  drilled  a  number  of  small  holes  in  the  manner 
shown  in  Fig.  22.     It  is  preferable,  when  it  is  possible,  to  take  steam  in 

this  manner  from  a  vertical  pipe  and  better  to 
take  it  from  a  pipe  in  which  the  current  of 
steam  is  rising  rather  than  from  one  in  which 
it  is  descending.  Fortunately,  the  two  points 
in  a  boiler  plant  where  it  is  most  necessary  to 
make  determinations  of  the  quality  of  steam 
are  the  point  where  the  steam  issues  from  the 
boiler  and  the  point  where  the  steam  enters 
the  engine.  In  the  first  case,  the  steam  is  of 
uniform  quality,  and  it  is  almost  always  pos- 
sible to  take  the  sample  from  a  vertical  pipe. 
In  the  second  case,  the  steam  is  usually  passed 
through  a  separator  before  entering  the  engine, 
and  the  action  of  the  separator  is  such  that 
the  steam  entering  the  engine  is  uniform  in 
quality.  If  any  suspicion  exists  that  the  steam 
is  not  uniform  in  quality,  great  pains  must  be  taken  to  insure  that  the 
sample  truly  represents  the  actual  quality  of  the  steam. 

114.  Other  Calorimeters.  In  case  the  amount  of  moisture  in  the  steam 
is  large,  the  quality  of  the  steam  may  be  determined  by  condensing  the 
steam  in  a  known  weight  of  water  and  determining  the  rise  in  temperature. 
A  calorimeter  operating  on  this  principle  is  known  as  a  barrel  calorimeter. 
Into  a  known  weight  of  water  in  a  barrel  is  introduced  a  pipe  through 
which  steam  flows.  The  condensation  of  the  steam  raises  the  temperature 
of  the  water  and  the  heat  lost  by  the  steam  is  equal  to  the  heat  gained 
by  the  water.  Let  W  be  the  weight  of  water  originally  contained  in  the 
barrel,  and  w  be  the  gain  in  weight  or  weight  of  steam  condensed.  Let 
t\  be  the  initial  temperature  of  the  water,  and  t2  be  the  final  temperature 
of  the  water.  Let  hi  and  h2  be  the  heat  of  the  liquid  (as  obtained  from 
a  steam  table)  at  the  temperature  t\  and  t2  respectively.  Let  L  be  the 
latent  heat  of  evaporation  of  dry  and  saturated  steam  at  the  pressure 
of  the  steam  which  is  sampled,  and  ^3  be  the  heat  of  the  liquid  at  this 
pressure.  The  heat  gained  by  the  water  will  then  be  WQi^  —  hi)  and  the 
heat  lost  by  the  steam  will  be  w(qL -\-hs~- h2)  since  the  steam  is  con- 
densed and  the  liquid  reduced  to  the  temperature  corresponding  to  h2. 
Equating  these  expressions  and  solving  for  q,  we  will  have 


wL 

The  barrel  calorimeter  is  not  as  accurate  an  instrument  as  the  throttling 
calorimeter,  but  if   properly  used   it  will  give  fairly  good  results.     The 


ART.  114 


OTHER  CALORIMETERS 


85 


accuracy  of  the  calorimeter  will  obviously  depend  upon  the  accuracy  of 
the  thermometer  readings,  and  of  the  weight  obtained,  upon  a  thorough 
stirring  of  the  water  in  the  barrel  so  that  all  parts  are  of  the  same  tempera- 
ture, and  upon  the  length  of  time  which  the  experiment  takes.  The 
shorter  the  time  of  the  experiment,  other  things  being  equal,  the  more 
accurate  the  results  will  be.  The  barrel  calorimeter  usually  gives  results 
which  are  too  low. 

The  separating  calorimeter  is  an  instrument  which  mechanically 
separates  the  water  from  the  steam.  The  water  is  then  weighed  or  meas- 
ured and  the  steam  is  weighed  or  estimated  in  some  way.  The  weight 
of  steam  divided  by  the  weight  of  water  plus  the 
weight  of  steam  gives  the  quality  of  the  steam. 
Carpenter's  separating  calorimeter,  shown  in  Fig. 
23,  is  an  example  of  this  class.  The  steam  enters 
the  instrument  at  the  top  and  issues  into  the 
body  of  the  calorimeter  through  the  several  holes 
in  the  pipe  A.  When  the  direction  of  motion 
of  the  steam  is  suddenly  changed,  by  causing  the 
steam  to  pass  out  of  the  chamber  B  in  an  upward 
direction,  the  superior  inertia  of  the  heavy 
particles  of  water  carries  them  against  the  per- 
forated metal  basket  C,  to  which  they  adhere. 
The  water  so  collected  drips  into  the  chamber  D, 
where  it  is  measured  by  means  of  the  gage  glass 
E.  The  dry  steam  following  the  path  shown  by 
the  arrow  escapes  through  an  orifice  at  the 
bottom  of  the  calorimeter.  It  may  be  shown 
experimentally  that  so  long  as  the  pressure  in  the 
calorimeter  is  more  than  twice  that  of  the  atmos- 
phere, the  weight  of  steam  escaping  through 
this  orifice  in  a  given  time  is  very  nearly  pro- 
portional to  the  absolute  pressure  of  the  steam  in  the  calorimeter.  This 
absolute  pressure  is  measured  by  the  steam  gage  G.  The  weight  of  dry 
steam  discharged  in  a  given  time  is  then  given  by  the  formula, 

W  =  Ktp, 

where  K  is  the  discharge  constant,  t  is  the  time  (in  minutes)  and  p  is  the 
absolute  pressure  in  the  calorimeter.  K  is  to  be  determined  for  any 
particular  instrument,  by  condensing  the  steam  discharged  at  known 
pressure  in  a  known  time.  If  w  be  the  weight  of  water  collected  in  the 
calorimeter  in  time  t,  the  quality  of  the  steam  will  be 

W 


FIG.    23. — Carpenter's 
separating  calorimeter 


86 


WET  AND  SUPERHEATED  VAPORS 


ART.  115 


The  errors  of  the  separating  calorimeter  are  those  due  to  radiation  and 
those  due  to  incomplete  separation  of  the  water  from  the  steam.  These 
two  sources  of  error  tend  to  correct  one  another,  and  the  latter  is 
usually  greater  in  amount  than  the  former,  so  that  the  apparent  quality,  as 
obtained  by  the  use  of  the  separating  calorimeter,  is  usually  greater  than 
the  true  quality.  The  separating  calorimeter  is  a  convenient  instrument 
to  use,  but  its  discharge  constant  and  its  errors  should  be  determined 
before  the  instrument  is  used. 

The  quality  of  steam  may  be  obtained  by  drying  and  superheating 
it  by  means  of  a  measured  quantity  of  electrical  energy,  as  is  done  in  the 
Thomas  superheating  calorimeter.  Various  types  of  steam  calorimeters 
and  the  proper  methods  of  using  them  are  described  in  Carpenter's  Exper- 
imental Engineering,  Chapter  13. 


FIG.  24. 


FIG.  25. 


115.  The  Steam  Separator.  It  is  usual,  when  steam  engines  are 
distant  from  the  boilers  supplying  them  with  steam,  or  when  for  any 
reason  the  steam  supply  is  likely  to  be  wet,  to  interpose  in  the  steam  pipe, 
close  to  the  engine,  an  apparatus  termed  a  separator,  whose  duty  it  is  to 
remove  from  the  steam  the  most  of  the  water  which  it  contains.  Sepa- 
rators operate  on  two  principles.  In  the  first  type  the  steam  passes  into 
the  separator  at  high  velocity  and  its  direction  is  suddenly  changed.  The 
wet  steam  consists  a  mixture  of  vapor  and  water.  The  particles  of  water 
being  many  hundred  times  heavier  than  the  steam,  their  superior  inertia 
will  cause  them  to  shoot  straight  ahead  when  the  current  of  steam  is 
suddenly  deflected.  If  these  particles  of  water  encounter  a  wet  surface, 
t^ey  will  adhere  to  the  surface  and  drip  to  the  bottom  of  the  chamber  in 
which  it  is  contained.  Such  a  separator  is  shown  in  Fig.  24. 


ART.  115  PROBLEMS  87 

In  the  second  type  of  steam  separator,  the  steam  is  caused  to  travel 
in  a  helical  path;  the  centrifugal  force  so  developed,  on  account  of  the 
superior  density  of  the  water  particles,  throws  them  against  the  outside 
walls  of  the  separator,  upon  which  they  collect.  The  water  then  drips 
to  the  bottom  of  the  separator.  Such  a  separator  is  illustrated  in  Fig.  25. 

A  separator  will  usually,  in  case  very  wet  steam  is  supplied  to  it, 
deliver  steam  of  98  per  cent  quality  or  better.  In  case  the  steam  is 
fairly  dry  (i.e.,  of  96  per  cent  quality  or  better)  the  greater  part  of  the 
moisture  present  will  be  extracted  by  the  separator.  Steam  containing 
less  than  2  per  cent  of  moisture  is  usually  known  as  commercially  dry 
steam.  Such  steam  may  be  always  obtained  by  the  use  of  a  suitable 
separator.  The  water  which  collects  in  a  separator  must  be  drawn  away 
at  intervals,  for,  if  the  separator  fills  up  with  water,  it  is  no  longer  effective. 
The  water  from  a  separator  is  usually  taken  care  of  by  an  automatic  device 
termed  a  steam  trap,  which  discharges  the  water  flowing  into  it,  at  inter- 
vals, without  permitting  the  escape  of  steam. 


PROBLEMS 

1.  How  much  water  is  contained  in  8  Ibs.  of  wet  steam  whose  quality  is  85%? 

Ans.     1.2  Ibs. 

2.  What  weight  of  dry  and  saturated  steam  is  contained  in  10  Ibs.  of  wet  steam 
having  15  per  cent  of  moisture?  Ans.     8.5  Ibs. 

3.  What  is  the  heat  of  the  liquid  of  wet  steam  at  a  pressure  of  1  atmosphere? 

Ans.     180  B.T.U. 

4.  What  is  the  latent  heat  of  evaporation  of  1  Ib.  of  steam  of  90  per  cent  quality 
at  a  pressure  of  1  atmosphere?  Ans.     873.4  B.T.U. 

5.  What  is  the  total  heat  of  1  Ib.  of  steam  of  90  per  cent  quality  at  a  pressure  of 
]  atmosphere?  Ans.     1053.4  B.T.U. 

6.  What  is  the  specific  volume  of  steam  of  90  per  cent  quality  at  a  pressure  of 
1  atmosphere?  Ans.     26.93  cu.ft. 

7.  What  is  the  density  of  steam  of  90  per  cent  quality  at  a  pressure  of  1  atmosphere? 

Ans.     0.0416  Ibs.  per  cu.ft. 

8.  What  is  the  external  work  of  evaporation  of  steam  of  90  per  cent  quality  at  a 
pressure  of  1  atmosphere?  Ans.     65.5  B.T.U. 

9.  What  is  the   internal  energy  of  evaporation    of  steam    of  90  per  cent  quality 
at  a  pressure  of  1  atmosphere?  Ans.     807.8  B.T.U. 

10.  What  is  the  total  internal  energy  of  steam  of  90  per  cent  quality  at  a  pressure 
of  1  atmosphere?  Ans.     987.8  B.T.U. 

11.  What  is  the  entropy  of  the  liquid  of  steam  of  90  per  cent  quality  at  a  pressure 
of  1  atmosphere?  Ans.     0.3118. 

12.  What  is  the  entropy  of  evaporation  of  steam  of  90  per  cent  quality  at  a  pressure 
of  1  atmosphere?  Ans.     1.3003. 

13.  What  is  the  total  entropy  of  steam  of  90  per  cent  quality  at  a  pressure  of 
1  atmosphere?  Ans.     1.6121. 

14.  The  latent  heat  of  evaporation  of  wet  steam  for  a  temperature  of  300°  is  800 
B.T.U.     What  is  its  quality?  Ans.     88%. 


88  WET  AND   SUPERHEATED   VAPORS  ART.  115 

15.  The  total  heat  of  wet  steam  at  a  pressure  of  100  Ibs.  is  1100  B.T.U.     What 
is  its  quality?  Ans.     90.3%. 

16.  Two  pounds  of  wet  steam  are  contained  in  a  volume  of  12.96  cu.ft.  at  a 
temperature  of  280°.     What  is  the  quality?  Ans.     75%. 

17.  Wet  steam  is  found  to  weigh  0.120  Ibs.  per  cubic  foot  at  a  pressure  of  50  Ibrf. 
What  is  its  quality?  Ans.     98%. 

18.  The  entropy  of  evaporation  of  wet  steam  at  a  temperature  of  180°  is  1.400. 
What  is  its  quality?  Ans.     90.5%. 

19.  The  total  entropy  of  wet  steam  at  a  temperature  of  330°  is  1.400.     What  is 
its  quality?  Ans.     82.1.%. 

20.  Steam  having  a  pressure  of  150  Ibs.  per  square  inch  has  a  temperature  of 
408.5°.     What  is  the  amount  of  superheat?  Ans.     50°. 

21.  Assuming  the  specific  heat  of  superheated  steam  at  atmospheric  pressure  to 
be  0.47,  what  will  be  the  heat  of  superheat  of  1  Ih.  of  steam  at  a  temperature  of  312° 
and  a  pressure  of  1  atmosphere?  Ans.     47  B.T.U. 

22.  What  will  be  the  total  heat  of  this  steam?  Ans.     1197.4  B.T.U. 

23.  From  a  table  of  the  properties  of  superheated  steam  find  the  specific  volume, 
the  total  heat,  and  the  entropy  of  steam  of  100  Ibs.  pressure  and  having  a  temperature 
of  427.8°.  Ans.     5.14  cu.ft.,  1239.7  B.T.U.,  and  1.6658. 

24.  From  such  a  table  determine  the  temperature  of  steam  whose  pressure  is 
120  Ibs.  and  whose  total  heat  is  1233.8  B.T.U.  Ans.     421.3°. 

25.  Determine  the  number  of  degrees  of  superheat  of  steam  of  150  Ibs.  pressure 
whose  entropy  is  1.6343.  Ans.     100°. 

26.  What  quantity  of  heat  is  required  to  raise  1  Ib.  of  water  from  a  temperature 
of  60°  to  a  temperature  of  212°?  Ans.     151.92  B.T.U. 

27.  What  quantity  of  heat  is  required  to  evaporate  1  Ib.  of  water  of  a  temperature 
of  60°  into  dry  and  saturated  steam  at  a  temperature  of  212°?    Ans.     1122.3  B.T.U. 

28.  What  quantity  of  heat  will  be  required  to  evaporate  10  Ibs.  of  water  having  a 
temperature  of  80°  into  steam  of  90  per  cent  quality  at  a  pressure  of  100  Ibs.  absolute? 

Ans.     10,423  B.T.U. 

29.  What  quantity  of  heat  will  be  required  to  evaporate  100  Ibs.  of  water  of  a 
temperature  of  60°  into  steam  at  a  pressure  of  150  Ibs.  and  a  temperature  of  448.5°? 

Ans.     121,630  B.T.U. 

30.  One  pound  of  steam  of  a  pressure  of  100  Ibs.  per  square  inch  and  a  quality 
of  50  per  cent  is  expanded  isothermally  until  it  is  dry  and  saturated.     Find  the  work 
done  and  the  heat  supplied.  Ans.     31,890  ft.-lbs.  and  444.0  B.T.U. 

31.  Steam  having  a  volume  of  2  cu.ft.  and  a  pressure  of  100  Ibs.  is  expanded  while 
it  remains  in  a  dry  and  saturated  condition  to  a  pressure  of  10  Ibs.     What  is  its  final 
volume?  Ans.     17.33  cu.ft. 

32.  Dry  and  saturated  steam  at  a  pressure  of  100  Ibs.  expands  adiabatically  until 
its  pressure  is  10  Ibs.     What  is  its  final  total  entropy,  entropy  of  evaporation,  and 
quality?  Ans.     1.6002,  1.3188,  and  87.67%. 

33.  What  will  be  the  total  heat  of  the  steam  when  the  expansion  has  proceeded  to 
2  Ibs.  absolute?  Ans.     930.0  B.T.U. 

34.  Steam  having  a  quality  of  10  per  cent  is  compressed  adiabatically  from  a 
pressure  of  10  Ibs.  absolute  to  a  pressure  of  30  Ibs.  absolute.     What  is  its  quality? 

Ans.     4.9%. 

35.  At  what  pressure  will  this  steam  become  completely  transformed  into  water? 

Ans.     64.4  Ibs. 

36.  What  quantity  of  work  was  performed  in  compressing  this  wet  steam  to  a 
pressure  of  64.4  Ibs.?  Ans.     14.6  B.T.U. 


ART.  115  PROBLEMS  89 

37.  What  quantity  of  work  is  performed  by  1  Ib.  of  steam  in  expanding  adiabati- 
cally  from  a  temperature  of  300°  to  a  temperature  of  100°,  the  steam  being  initially 
dry  and  saturated?  Ans.     239.1  B.T.U. 

38.  Steam  in  a  throttling  calorimeter  has  a  temperature  of  312°  at  a  pressure  of 
1  atmosphere.     What  is  its  total  heat?  Ans.     1197.4  B.T.U. 

39.  The  original  pressure  of  this  steam  was  200  Ibs.  per  square  inch.     What  was 
its  quality  before  entering  the  calorimeter?  Ans.     99.9%. 

40.  The  temperature  of  the  steam  in  a  throttling  calorimeter  is  220°  when  the 
barometer  indicates  a  pressure  of  13  Ibs.  per  square  inch.     The  original  pressure  of 
the  steam  was  87  Ibs.  gage.     Find  the  quality  of  the  steam.  Ans.     96.91%. 

41.  A  barrel  contains  400  Ibs.  of  water  at  a  temperature  of  75°  F.     After  con- 
densing steam  at  a  pressure  of  120  Ibs.  absolute,  it  gains  20  Ibs.  in  weight  and  53° 
in  temperature.     Find  the  quality  of  the  steam.  Ans.     95.8%. 


CHAPTER  VII 

MIXTURES    OF    GASES    AND    VAPORS 

116.  Gaseous   Mixtures.     When  two  or  more  sensibly  perfect  gases 
are  brought  into  contact  with  one  another,  the  particles  of  one  tend  to 
pass  between  the  particles  of  the  other.     As  a  result,  after  the  lapse  of  a 
sufficient  length  of  time,  the  two  gases  will  form  a  homogeneous  mechanical 
mixture.     This  process  of  mixing  is  known  as  diffusion,  and  the  mixture 
resulting  is,  in  every  sense  except  a  chemical  one,  a  perfectly  homogene- 
ous body,  and  will  remain  so  provided  it  undergoes  no  chemical  action, 
and  its  component  particles  are  not  separated  by  enclosing  the  mixture 
within  a  porous  vessel.1      When  such  a  mixture  of  gases  occurs,  all  of 
the  constituents  of  the  mixture  will  come  to  the  same  temperature,  and 
this  temperature  will,   of  course,   be  the  temperature   of  the  mixture. 
The  mass  of  the  mixture  will  be  the  sum  of  the  masses  of  the  several 
constituents.     If  the  mixture  be  confined  within  a  vessel,  each  of  the 
constituents  will  exert  upon  the  walls  a  pressure  which  is  equal  in  amount 
to  the  pressure  which   that   constituent  would    exert  were  it   confined 
separately  within  the  vessel,  at  the  same  temperature.     Consequently, 
the  pressure  of  the  mixture  will  be  the  sum  of  the  pressures  of  the  several 
constituents.     Were  each  of  the  constituents  confined   at  the  pressure 
and  the  temperature  of  the  mixture,  they  would  occupy  definite  volumes. 
The  sum  of  these  volumes  will,  if  the  constituents  are  all  sensibly  perfect 
gases,  be  the  volume  of  the  mixture. 

117.  The  Thermal  Properties  of  Gaseous  Mixtures.     The  density  of 
such  a  mixture,  under  given  conditions,  may  be  obtained  by  dividing 
the  mass  of  the  mixture  by  its  volume,  or  if  the  masses  of  the  several 
constituents  are  known,  by  dividing  the  sum  of  the  products  of  the  mass 
and  density  of  each  of  the  constituents,  under  the  given  conditions,  by 
the  mass  of  the  mixture.     From  the  density  of  the  mixture  the  value 
of  R  for  the  mixture  may  be  deduced  by  the  method  given  in  Art.  30. 
In  the  same  way,  the  specific  heat  of  such  a  mixture  at  constant  pressure 
(or  constant  volume)  may  be  found  by  dividing  the  sum  of  the  products 
of  the  mass  and  specific  heat  at  constant  pressure  (or  constant  volume) 
of  each  of  the  constituents,  by  the  mass  of  the  mixture.     The  value  of 

1  The  process  of  separating  the  constituents  of  a  gaseous  mixture  by  the  action 
of  a  porous  wall  is  termed  osmosis.     For  the  theory  of  this  action  see  Chapter  XXVI. 

90 


ABT.  117  THE  THERMAL  PROPERTIES  OF  GASEOUS   MIXTURES          91 

the  constant  f  for  a  mixture  of  gases  is  the  ratio  of  the  specific  heats  at 
constant  pressure  and  constant  volume,  and  the  mixture  will,  during 
expansion  or  compression,  behave  exactly  as  if  it  were  a  simple  gas  whose 
thermodynamic  properties  are  those  obtained  in  the  manner  given  above. 
We  may,  therefore,  treat  such  a  mixture  as  if  it  were  a  gas  having 
definite  and  known  thermodynamic  properties. 

The  mathematical  statement  of  the  properties  of  two  or  more  gases 
may  be  obtained  as  follows  :  Let  W  and  W"  be  the  mass  of  the  two  con- 
stituents, Rf  and  R"  the  value  of  the  function  R  for  these  constituents, 
D'  and  D"  the  density  of  these  constituents  under  standard  conditions, 
K'p  and  Kn  'p  the  specific  heat  at  constant  pressure,  and  K'  v  and  K"  v 
the  specific  heat  at  constant  volume  of  the  two  constituents.  We  will 
then  have  the  following  relations  : 

The  mass  of  the  mixture  will  be 

W=W'+  W"  .............     (1) 

When  the  mixture  is  within  the  volume  V  at  the  temperature  T,  the  pres- 
sure of  the  mixture  will  be 

P=^(W'R'+W"R")  ........     ...     (2) 

The  density  of  the  mixture  under  standard  conditions  will  be 

W'D'  +  WD" 

W'  +  W" 


The  specific  heat  of  the  mixture  at  constant  volume  will  be 


KV'W'+KV"W" 


For  the  specific  heat  of  the  mixture  at  constant  pressure,   we  will 
have  the  value 


KP'W'+KP"W" 


The  ratio  of  these  two  quantities  gives  the  value  of  f  for  the  mixture, 
which  becomes 

_KP'W'+KP"W» 
r  '  KV'W  +  KV"W"' 

The  value  of  R  for  the  mixture  will  of  course  be  equal  to 

R=K,-K,,    .............     (7) 


or 


KP'W'+KP"W"  _  KV'W  +  K9"W" 
W  +  W"  W  +W"       > 


92  MIXTURES  OF  GASES  AND  VAPORS  ART.  119 

which  becomes 

p  _  W'(KP'  -  Kv')  +  W"(KP"  -  Kv") 

W  +  W" 
which  is  of  course 

R=  ^W'++RW^~ <10) 

An  inspection  of  equation  (6)  will  show  that  the  value  of  f  for  the  mixture 
of  gases  is  not  the  weighted  mean  of  the  values  of  this  constant  for  the 
constituents  of  the  mixture,  as  might  be  supposed,  from  analogy  with  the 
other  quantities.  When  there  are  more  than  two  constituents  present 
in  the  mixture,  its  properties  may  be  determined  by  properly  modifying 
the  above  equations.  For  instance,  for  a  mixture  of  three  gases  the  value 
of  R  becomes 

R'W  +  n"W"  +  R'"W" 
W  +  W"  +  W" 

118.  Mixture  of  a  Gas  with  a  Vapor.     A  mixture  of  a  gas  and  a  vapor 
becomes  homogeneous  through  diffusion  in  exactly  the  same  way  as  do 
mixtures  of  two  or  more  gases.     The  pressure  exerted  by  the  mixture 
upon  the  walls  of  the  containing  vessel  is  the  sum  of  the  pressures  which 
would  be  exerted  by  the  gas  and  the  vapor  were  each  one  contained 
separately  in  the  vessel  at  the  given  temperature.     If  the  vapor  be  sat- 
urated on  account  of  the  presence  of  its  liquid,  the  pressure  which  it  exerts 
will  depend  upon  the  temperature,  while  the  pressure  which  the  gas  will 
exert  will  depend  upon  its  volume  and  mass  as  well  as  on  the  temperature . 
We  may  then  compute  the  pressure  exerted  by  the  gas  by  subtracting 
from  the  pressure  of    the  mixture  the  saturation  pressure  of  the  vapor 
at  the  temperature  of  the  mixture.     In  case  the  vapor  is  superheated, 
the  pressure  exerted  will,  as  before,  be  the  sum  of  the  pressures  of  each 
constituent  of  the  mixture,  but  the  pressure  of  the  superheated  vapor 
depends,  like  that  of  the  gas,  upon  the  mass  of  the  vapor  and  the  volume 
in  which  it  is  confined,  and  the  pressure  of  the  vapor  may  be  obtained  only 
by  the  methods  described  in  Art.  101. 

119.  Air  a  Mixture  of  Gases  and  Water  Vapor.     The  thermal  proper- 
ties of  air,  as  given  in  Chapter  II.,   are  those  of  dry  air,  free  from  carbon 
dioxide.     Outdoor  air  usually  contains  a  minute  percentage  (.03  per  cent) 
of  carbon  dioxide  and  a  variable  quantity  of  water  vapor,   so  that  the 
density,  specific  heat,  and  other  thermal  properties  of  the  atmosphere  are 
continually  varying.     Ordinarily,  the  properties  of  air  may  be  assumed  to 
be  those  of  dry  air  free  from  carbon  dioxide,  without  sensible  error.     In 
certain  classes  of  engineering  computations,  however,  it  is  essential  to 
take  account  of  the  variation  in  the  properties  of  air  when  varying  quan- 
tities of  water  vapor  are  present.     In  such  computations  it  is  necessary 


, 

ART.  120  HUMIDITY   OF  AIR  93 

to  consider  air  as  a  mixture  of  a  gas  of  known  properties,  with  superheated 
water  vapor  or  steam. 

120.  Humidity  of  Air.     When  the  pressure  of  the  water  vapor  present 
in  the  air  is  the  saturation  pressure  of  water  vapor  at  the  temperature 
of  the  air,  the  air  is  said  to  be  saturated.     If  the  pressure  is  less  than  this 
quantity,  the  air  is  said  to  have  a  certain  humidity,  which  is  expressed 
as  a  per  cent  and  is  found  by  dividing  the  actual  pressure  of  the  water 
vapor  in  the  air  by  the  saturation  pressure  of  water  vapor  at  the  temper- 
ature of  the  air.     In  case  the  air  is  saturated,  it  contains  all  the  moisture 
which  it  is  possible  for  it  to  hold,  and  any  reduction  in  temperature  will 
precipitate  some  of  the  moisture  in  the  form  of  dew  or  rain.     In  case 
the  humidity  of  the  air  is  less  than  100  per  cent,  the  water  vapor  present 
in  the  air  is  superheated,  since  its  temperature  is  greater  than  the  tem- 
perature corresponding  to  its  pressure,  and  the  air  may  be  treated  as  a 
mixture  of  a  gas  and  a  superheated  vapor. 

121.  Dew  Point.     If  a  cold  metallic  surface  be  exposed  to  moist  air, 
dew  will  gather  upon  it,  if  its  temperature  is  less  than  the  saturation 
temperature  of  the  water  vapor  present  in  the  air.     The  maximum  tem- 
perature at  which  .moisture  will  appear  upon  such  a  surface  is  known  as 
the  dew  point.     If  the  dew  point  be  determined,  we  may,  from  a  steam 
table,  find  the  pressure  of  the  water  vapor  present  in  the  air.     The  dif- 
ference  between   the  dew  point  and  the  air  temperature  is  the  super- 
heat of  the  water  vapor  present  in  the  air.     From  the  pressure  and  super- 
heat of  this  vapor  we  may  determine  its  density,  which  will  be  the  weight 
of  water  vapor  present  per  cubic  foot  of  air. 

122.  The  Wet-bulb  Hygrometer.     The  humidity  of  the  air  is  usually 
determined  by  means  of  an  apparatus  called    a  wet-bulb  hygrometer. 
This  instrument  consists  of  two  thermometers  both  protected  from  the 
direct  radiation  of  the  sun  or  other  objects  reflecting  heat.     The   bulb 
of  one  of  these  thermometers  is  surrounded  by  air.     The  bulb  of  the 
other  is  enveloped  in  lamp  wicking  which  dips  into  a  cup  of  water.     This 
thermometer  must  be  so  situated  that  the  air  has  free  access  to  the  wicking, 
but  must  not  be  exposed  to  wind.     The  water  contained  in  the  wicking, 
being  in  contact  with  the  air,  will  evaporate  and  more  will  be  drawn  up 
to  take  its  place.     In  evaporating,  the  water  appropriates  the  sensible 
heat  of  surrounding  objects  and  reduces  the  temperature  of  the  ther- 
mometer bulb  below  that  of  the  air.     From  the  difference  in  temperature 
indicated  by  the  dry  bulb-thermometer,  the  dew-point  and  the  relative 
humidity  may  be  computed.     Since  the  wet-bulb  thermometer  receives 
heat  by  radiation  from  surrounding  objects  and  the  pressure  of  the  water 
vapor  in  its  neighborhood,  due  to  the  continual  evaporation,  is  higher 
than  elsewhere,  it  will  not  indicate  a  temperature  as  low  as  the  dew-point. 
It  is  necessary,  therefore,  to  make  use  of  the  following  empirical  table  in 


94 


MIXTURES   OF   GASES   AND   VAPORS 


AKT.  123 


determining  the  humidity  of  the  air  from  the  indications  of  the  wet-bulb 
thermometer: 


RELATIVE   HUMIDITY  ,  PER  CENT 


Difference  between  the  Dry  and  the  Wet  Thermometers,  Deg.  F. 

Dry 

Ther- 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

>>•> 

23 

24 

26 

28 

30 

mometer, 

Dee1  F 

.  Relative  Humidity,  Saturation  being  100.  (Barometer  =  30  ins.) 

32 

89 

7!) 

69 

59 

49 

39 

30 

20 

11 

2 

40 

92 

83 

75 

68 

60 

52 

45 

37 

29 

23 

15 

7 

0 

50 

93 

«S7 

SO 

74 

67 

61 

55 

49 

43 

38 

32 

27 

21 

16 

11 

5 

0 

60 

94 

89 

83 

78 

73 

68 

63 

58 

53 

48 

43 

39 

34 

30 

26 

21 

17 

13 

9 

5 

1 

70 

95 

90 

8(5 

81 

77 

72 

68 

64 

59 

55 

51 

48 

44 

40 

36 

33 

29 

25 

22 

19 

15 

12 

9 

6 

80 

96 

91 

87 

83 

79 

75 

72 

68 

64 

61 

57 

54 

50 

47 

44 

41 

38 

35 

32 

29 

26 

23 

20 

18 

12 

7 

90 

96 

92 

89 

85 

81 

78 

74 

71 

68 

65 

61 

58 

55 

52 

49 

47 

44 

41 

39 

36 

34 

31 

29 

26 

22 

17 

13 

100 

96 

93 

89 

86 

S3 

80 

77 

73 

70 

68 

65 

62 

59 

56 

54 

51 

49 

46 

44 

41 

39 

37 

35 

33 

28 

24 

21 

110 

97 

03 

90 

87 

84 

81 

78 

75 

73 

70 

67 

65 

62 

60 

57 

55 

52 

50 

48 

46 

44 

42 

40 

38 

34 

30 

26 

120 

97 

94 

91 

88 

85 

82 

80 

77 

74 

72 

69 

67 

65 

62 

(50 

58 

55 

53 

51 

49 

47 

45 

43 

41 

38 

34 

31 

140 

97 

95 

92 

89 

87 

84 

82 

79 

77 

75 

73 

70 

68 

(56 

64 

62 

60 

58 

56 

54 

53 

51 

49 

47 

44 

41 

38 

From  Kent's  "  Pocket  Book,"  1910  Edition. 

123.  Normal  Humidity  of  the  Atmosphere.     Except     in    very   arid 
regions,  the  humidity  of  the  air  varies  from  40  to  80  per  cent,  usually 
ranging  from  60  to  70  per  cent  in  inland  districts  and  from  70  to  80  per 
cent  by  the  sea.     Consequently,  air  is  always  ready  to  absorb  moisture, 
and  when  water  is  exposed  to  the  action  of  the  air  it  will  be  evaporated. 
The  rate  of  this  evaporation  will  depend  upon  the  humidity  and  temper- 
ature of  the  air,  and  upon  the  amount  of  wind.     By  warming  air,  its 
humidity  will  be  greatly  diminished  and  its  power  to  absorb  moisture 
correspondingly    increased.     Drying    kilns,    cooling    towers,    and    other 
forms  of  engineering  apparatus  depend  upon  these  principles  for  their 
operation. 

124.  The  Computation  of  the  Properties  of  Moist  Air.      When  the 
relative  humidity  is  known,  the  pressure  of  the  water  vapor  present  in 
the  air  may  be  found  by  multiplying  the  saturation  pressure  of  water 
vapor  at  the  temperature  of  the  air,  as  obtained  from  a  steam  table,  by 
the   relative   humidity.     The   saturation   temperature   corresponding   to 
this  pressure  is  the  dew-point.     Conversely  the  humidity  may  be  found 
by  dividing  the  saturation  pressure  at  the  temperature  of  the  dew-point 
by  the  saturation  pressure  at  the  temperature  of  the  air.     The  density 
of  the  water  vapor  in  the  air  may  be  found  by  multiplying  the  density  of 
water  vapor  at  the  dew-point  by  the  absolute  temperature  of  the  dew- 


ART.  124  PROBLEMS  95 

point,  and  divided  by  the  absolute  temperature  of  the  air.  Almost 
exactly  the  same  result  will  be  obtained  by  multiplying  the  density  of 
water  vapor  at  the  temperature  of  the  air  by  the  relative  humidity,  and 
since  this  method  is  both  very  exact  and  very  convenient,  it  is  proper 
to  employ  it  in  engineering  computations. 

The  pressure  of  the  dry  air  present  in  the  atmosphere  may  be  found 
by  subtracting  the  pressure  of  the  water  vapor  from  the  atmospheric 
pressure  indicated  by  the  barometer.  The  density  of  the  dry  air  (i.e., 
its  weight  per  cubic  foot)  may  be  found  from  its  absolute  pressure  and 
temperature  by  means  of  the  characteristic  equation  of  gases,  PV=  WRT. 
Adding  together  the  density  of  the  water  vapor  and  the  density  of  the 
dry  air,  we  will  have  the  weight  of  the  atmosphere  in  pounds  per  cubic 
foot. 

The  principles  which  have  been  developed  in  the  preceding  paragraphs 
with  regard  to  the  pressure,  density,  etc.,  of  the  constituents  of  the  atmos- 
phere may  be  applied,  with  equal  propriety,  in  the  case  of  any  mixture 
of  gas  and  vapor. 

PROBLEMS 

1.  A  volume  of  10  cu.ft.  contains  1  Ib.  of  hydrogen  and  2  Ibs.  of  nitrogen  at  a 
temperature  of  550°  absolute.     Find  the  pressure  of  the  hydrogen,  of  the  nitrogen, 
and  of  the  mixture. 

Ans.     42,400  Ibs.  per  square  foot,  6060  Ibs.  per  square  foot,  and  48,460  Ibs.  per 
square  foot. 

2.  One  pound  of  carbon  monoxide  and  1  Ib.  of  marsh-gas  are  together  contained 
in  a  volume  of  4  cu.ft.  at  a  pressure  of  100  Ibs.  per  square  inch.     Find  the  pressure  of 
each  constituent.         Ans.     36.3  Ibs.  per  square  inch  and  63.7  Ibs.  per  square  inch. 

3.  Find  the  density  of  the  mixture  under  standard  conditions. 

Ans.     0.0613  Ibs.  per  cubic  foot. 

4.  Find  the  specific  heat  of  the  mixture  at  constant  volume.  Ans.     0.3202. 

5.  Find  the  value  of  the  constant  R  for  the  mixture.  Ans.     75.79. 

6.  Find  the  value  of  the  constant  f  for  the  mixture.  Ans.     1.304. 

7.  A  mixture  of  air  and  saturated  water  vapor  is  contained  in  a  confined  space 
and  has  a  temperature  of  60°.     The  pressure  of  the  air  is  1  atmosphere.     Find  the 
pressure  of  the  mixture.  Ans.     14.952  Ibs.  per  square  inch. 

8.  A  mixture  of  air  and  saturated  water  vapor  in  a  confined  space  has  a  tem- 
perature of  80°  F.  and  a  pressure  of  1  Ib.  per  square  inch  absolute.     Find  the  pressure 
of  the  air.  Ans.     0.495  Ibs.  per  square  inch. 

9.  If  water  is  present  and  the  tempreature  of  the  mixture  is  increased  to  200°  F., 
what  will  be  the  pressure  of  the  air  of  the  water  vapor,  and  of  the  mixture? 

Ans.     0.605  Ibs.,  11.52  Ibs.,  and  12.125  Ibs. 

10.  The  temperature  of  the  air  is  70°,  the  dew-point  is  found  by  experiment  to 
be  50°,  find  the  humidity.  Ans.     49.1%. 

11.  What  quantity  of  water  vapor  will  be  contained  in  each  cubic  feet  of  air  at 
the  above  humidity?  Ans.     0.000564  Ibs. 

12.  One  thousand  cubic  feet  of  air  at  a  temperature  of  60°  and  a  humidity  of  70 
per  cent  are  compressed  into  a  volume  of  200  cu.ft.     What  weight  of  moisture  did 
the  air  contain  before  compression?  Ans.     0.58  Ibs. 


96  MIXTURES   OF   GASES   AND   VAPORS  ART.  124 

13.  What  weight  of  moisture  will  the  air  contain  at  the  same  temperature  and 
100  per  cent  humidity  after  compression?  Ans.     0.1656  Ibs. 

14.  What  quantity  of  water  will  be  precipitated  by  the  compression? 

Ans.     0.414  Ibs. 

15.  A  wet-bulb  hygrometer  gives  readings  of  75°  and  68°.     What  is  the  humidity? 

Ans.     70%. 

16.  If  the  pressure  indicated  by  the  barometer  is  14.40  Ibs.  absolute,  what  is  the 
pressure  of  the  dry  air?  Ans.     14.1  Ibs.  per  square  inch. 

17.  If  the  temperature  is  raised  to  150°  and  the  humidity  to  100  per  cent,  find  the 
final  volume  of  the  air  in  terms  of  the  original  volume.  Ans.     1.506. 


CHAPTER  VIII 
THE   STEAM   ENGINE 

125.  The  Mechanism  of  the  Steam  Engine.      A  steam-power   plant 

consists  of  a  boiler  for  the  generation  of  steam,  an  engine  for  the  partial 
transformation  of  the  heat  of  the  steam  into  mechanical  energy,  and  a 
condenser  into  which  the' waste  steam  is  discharged,  together  with  neces- 
sary auxiliary  apparatus.  The  place  of  the  condenser  may  be  taken  by 
the  atmosphere,  the  steam  being  discharged  into  the  air  against  the  bar- 
ometric pressure.  Fig.  26  shows  the  steam  engine  of  such  a  power  plant  in 
section,  the  engine  shown  being  equipped  with  what  are  termed  Corliss  valves. 
Various  other  types  of  valves  are  in  use  for  the  distribution  of  steam  to 
the  cylinder,  but  the  action  of  the  engine  is  most  readily  understood 
when  the  valves  are  of  the  type  shown.  In  the  figure,  the  steam  pipe  A 
carries  steam  from  a  boiler  to  the  engine.  In  this  pipe  is  placed  the  throttle 
valve  B,  which  is  for  the  purpose  of  shutting  off  steam  when  the  engine 
is  not  running.  When  this  valve  is  open,  steam  flows  from  the  pipe  'into 
the  steam  chest  C.  Leading  from  the  steam  chests  are  two  ports,  one  to 
each  end  of  the  cylinder  D.  These  ports  are  closed  by  two  valves  e  and 
e',  which  are  known  as  the  inlet  valves.  Within  the  cylinder  the  piston 
F  slides  back  and  forth,  being  propelled  alternately  in  each  direction  by 
the  pressure  of  the  steam.  A  movement  of  the  piston  from  one  end  of 
the  cylinder  to  the  other  is  termed  a  stroke.  Two  successive  strokes 
make  one  revolution  of  the  engine.  The  total  distance  traversed  by  any 
point  in  the  piston  during  a  stroke  is  called  the  length  of  stroke,  or  piston 
travel.  The  piston  rod  G,  which  is  fastened  to  the  piston,  transmits  the 
force  exerted  upon  the  piston  to  the  cross-head  H,  whence  it  is  trans- 
mitted by  the  connecting  rod  /  to  the  crank  Jt  which  is  keyed  to  the  shaft 
K.  Upon  this  shaft  is  fixed  a  fly-wheel,  and  the  shaft  revolves  in  two  or 
more  bearings.  As  the  piston  is  pushed  back  and  forth  by  the  steam, 
the  intermediate  mechanism  pushes  the  crank  forward  and  pulls  it  back, 
causing  the  shaft  to  revolve.  The  function  of  the  fly-wheel  is  to  make 
the  rate  of  rotation  as  uniform  as  possible  by  the  inertia  of  its  revolving 
mass,  and  to  carry  the  engine  over  the  "  dead  points  "  which  occur  when 
the  crank  and  connecting  rod  are  in  line  at  either  end  of  the  stroke,  at 
which  time  the  force  exerted  by  the  steam  has  no  tendency  to  turn  the 

97 


98 


THE   STEAM   ENGINE 


ART.  125 


ART.  126  CYCLE  OF  OPERATIONS  99 

crank.  The  piston  is  a  cylindrical  body,  and  upon  the  outside  of  this 
cylinder  are  cut  grooves  into  which  are  fitted  piston  rings,  whose  function 
it  is  to  expand  against  the  side  of  the  cylinder  and  prevent  the  escape 
of  steam  past  the  piston.  The  cross-head  is  restrained  by  the  frame  of, 
the  engine  and  compelled  to  move  in  a  direction  parallel  to  the  axis  of 
the  cylinder.  A  port  termed  an  exhaust  port  leads  from  either  end  of  the 
cylinder  into  the  exhaust  pipe.  These  ports  are  closed  by  the  exhaust 
valves  M  and  M' '. 

126.  Cycle  of  Operations.  Assume  that  the  various  parts  of  the  engine 
are  each  in  the  position  shown  in  the  drawing,  the  inlet  valve  e  and  the 
exhaust  valve  M'  being  open.  Steam  will  enter  the  left-hand  end  (known 
as  the  head  end)  of  the  cylinder,  and  will  exert  a  pressure  upon  the  piston 
whose  total  amount  is  proportional  to  the  product  of  the  absolute  steam 
pressure  into  the  area  of  the  piston.  Since  this  pressure  is  greater  than  the 
pressure  upon  the  opposite  face  of  the  piston  (which  is  equal  only  to  the 
pressure  in  the  exhaust  pipe)  the  piston  will  be  forced  to  the  right,  rotating 
the  crank  in  a  clockwise  direction.  Steam  from  the  boiler  will  flow  into 
the  head  end  of  the  cylinder,  maintaining  the  pressure,  and  the  steam  con- 
tained in  the  opposite  or  crank  end  of  the  cylinder  will  escape  through  the 
exhaust  port  into  the  exhaust  pipe.  After  the  piston  has  moved  for- 
ward a  certain  amount  (usually  from  %  to  l/2  of  its  total  travel)  the  inlet 
valve  e  is  closed  by  the  mechanism  which  operates  it,  the  exhaust  valve 
Mf  remaining  open.  The  steam  which  is  contained  within  the  head  end 
of  the  cylinder  will  now  begin  to  expand,  increasing  in  volume  and  diminish- 
ing in  pressure,  and  this  expansion  will  continue  until  the  exhaust  valve 
is  opened  at  or  just  before  the  end  of  the  stroke.  At  some  point  near 
the  end  of  the  stroke,  which  is  known  as  the  forward  stroke,  the  exhaust 
valve  M'  is  closed,  and  just  at  the  end  of  the  stroke  the  exhaust  valve  M  is 
opened.  The  pressure  in  the  head  of  the  cylinder  now  drops  to  the  same 
value  as  the  pressure  in  the  exhaust  pipe,  the  steam  escaping  through 
valve  M.  The  pressure  in  the  right-hand  or  crank  end  of  the  cylinder 
begins  to  rise  on  account  of  the  compression  of  the  contained  steam,  as 
soon  as  the  valve  M'  is  closed,  and  at  the  end  of  the  stroke,  on  account 
of  the  introduction  of  steam  from  the  boiler  through  valve  e',  it  rises  to 
boiler  pressure.  The  pressure  upon  the  right-hand  face  of  the  piston 
now  drives  it  to  the  left,  causing  it  to  make  what  is  termed  the  return 
stroke.  At  the  proper  point  of  the  stroke  the  steam  supply  is  cut  off 
by  the  closing  of  valve  ef  and  the  steam  allowed  to  expand,  exactly  as 
in  the  head  end  of  the  cylinder.  As  the  piston  approaches  the  head  end 
of  the  cylinder,  the  valve  M  closes,  the  valve  M'  opens,  and  when  the 
crank  reaches  dead  center  (i.e.,  when  the  connecting  rod  and  crank  are 
in  the  line  and  the  piston  has  reached  the  limit  of  its  travel)  the  valve  e 
opens. 


100  THE   STEAM   ENGINE  ART.  127 

127.  Efficiency    of    the    Engine.     Each    succeeding   revolution    is    a 
repetition  of  the  events  of  the  preceding  one.     At  the  beginning  of  each 
working  stroke  a  definite  amount  of  steam  flows  into  one  end  of  the  cylin- 
der  from   the  boiler,  and  during  the  back   stroke  (or   exhaust   stroke,  as 
it  is  sometimes  called)  the  same  weight  of  steam  escapes  from  that  end 
of  the  cylinder  into  the  exhaust  pipe.     This  quantity  of  steam  is  called 
the  cylinder  feed  per  stroke,  or  simply  the   cylinder  feed.     The  weight  of 
steam  contained  in  the  cylinder  and  clearance  space  at  the  instant  the 
exhaust  valve   closes   is  called  the  cushion  steam.     The  working  stroke 
of  the    head  of  the  cylinder  is  the  back  stroke   of  the   crank   end,  and 
vice  versa.     The   heat  supplied   to   the  engine  in  a  given  time  is  equal 
to  the  heat  imparted  in  the  boiler  to  the  steam  which  is  used  by  the 
engine    during   that   time.      The   heat    rejected   by    the    engine    is    the 
latent  heat  of  the  steam  (which  is  usually  quite  wet)  which  is  rejected 
into  the  exhaust  pipe  during  the  same  period.     The  difference  between 
these  two   quantities   is   equal    to   the   heat  radiated   from  the    engine 
during  this  period   plus  the  work  done  by  the  engine  during  the  same 
period.      The   efficiency   of  the   engine  is  of  course  equal  to   the  work 
divided  by  the  heat  supplied.     It  is  apparent  that  water  must  be  supplied 
to  the  boiler  to  take  the  place  of  that  which  is  evaporated  by  the  boiler 
and  sent  to  the  engine.     The  water  so  supplied  is  termed  the  feed- water. 
This  water  may  and  should  have  almost  the  same  temperature  as  the 
exhaust  steam  which  the  engine  rejects,  since  this  exhaust  steam  may  be 
made  to  surround  tubes  through  which  the  feed-water  is  forced  on  its  way 
to  the  boiler,  or  some  other  method  of  heating  the  feed-water  by  the 
exhaust  steam  may  be  employed.     The  heat  supplied  by  the  boiler  to 
each  pound  of  steam  is  then  equal  to  the  total  heat  of  the  steam  (cor- 
rected, if  necessary,  for  wetness  or  superheat)  minus  the  heat  of  each 
pound  of  the  feed-water,  which  is  at  the  temperature  of  the  engine  exhaust. 
The  heat  rejected  per  pound  of  steam  is  the  latent  heat  of  the  wet  steam 
which  is  rejected.     The  generation  of  steam,  of  course,  costs  money,  both 
for  the  fuel  which  is  burned,  for  the  labor  necessary  in  burning  it  and 
caring  for  the  boiler,  and  for  other  necessary  expenses  of  operating  the 
boiler  plant.     It  is  therefore  highly  desirable  that  the  engine  should  be 
as  economical  as  possible  in  the  use  of  steam,  or  in  other  words,  that  it 
should  have  the  highest  possible  efficiency. 

128.  Types  of  Engines.     The  engine  described  in  the  preceding  para- 
graphs is  known  as  a  simple  non-condensing   engine  when   the   exhaust 
steam  is  rejected  into  the  air.     If  the  exhaust  steam  is  allowed  to  flow 
into  the  condenser  or  chamber  in  which  it  is  cooled  and  condensed,  and  in 
which  a  vacuum  pump  maintains  a  low  absolute  pressure,  the  engine  is 
said  to  be  a  condensing  engine.      Such  an  engine  is  usually  more  efficient 
than  a  non-condensing  engine. 


ART.  129 


THE   INDICATOR 


101 


It  has  been  found  that  it  is  both  more  convenient  and  more  economical 
to  allow  steam  to  pass  through  two  or  more  cylinders  in  succession,  in 
case  the  steam  pressure  is  high  and  the  engine  large.  The  first  cylinder, 
instead  of  exhausting  into  the  air  or  into  a  condenser,  exhausts  into  a 
closed  space  which  is  known  as  a  receiver.  The  steam  from  this  receiver 
flows  into  a  second  cylinder,  in  which  it  does  work,  and  is  finally  rejected 
to  the  air,  or  more  usually  to  a  condenser.  Sometimes  it  is  exhausted 
into  a  second  receiver  and  flows  from  this  into  a  third  cylinder  and  occa- 


FIG.  27. — Section  of  an  indicator. 

sionally  into  a  third  receiver,  and  thence  to  a  fourth  cylinder,  before 
entering  the  condenser.  When  the  steam  flows  through  two  cylinders 
in  succession  the  engine  is  said  to  be  compound.  When  it  flows  through 
three  cylinders  in  succession,  the  engine  is  said  to  be  triple  expansion, 
and  when  it  flows  through  four  cylinders  in  succession,  the  engine  is 
said  to  be  quadruple  expansion. 

129.  The  Indicator.  The  pressure-volume  diagram  of  the  working 
fluid  of  an  actual  steam  engine  or  other  thermodynamic  machine,  is 
termed  an  indicator  card.  An  indicator  card  is  obtained  from  an  engine 


102 


THE  STEAM   ENGINE 


ART.  129 


by  the  use  of  an  instrument  termed  an  indicator.  An  instrument  of  this 
kind  is  shown  in  section,  in  Fig.  27.  It  consists  of  a  hollow  cylinder  in 
which  is  a  piston  which  fits  rather  loosely,  so  as  to  move  without  fric- 
tion. This  piston  is  attached  to  one  end  of  a  small  helical  spring,  the 
other  end  of  which  is  fixed  to  the  upper  head  of  the  cylinder.  The 
pressure  of  the  steam  on  the  piston  forces  it  upward  against  the  resistance 
of  the  spring,  and  the  amount  by  which  the  piston  rises  will  be  strictly 
proportional  to  the  steam  pressure  producing  the  rise.  The  motion  of 
the  piston  is  transmitted  by  a  rod  to  the  parallel  motion  which  moves 


FIG.  28. — Indicator  reducing  motion. 

the  pencil  point.  The  motion  of  the  pencil  point  will  then  be  strictly 
proportional  to  the  steam  pressure  exerted  upon  the  piston.  The  pres- 
sure, in  pounds  per  square  inch  required  to  raise  the  pencil  point  a  distance 
of  one  inch,  is  termed  the  scale  of  the  spring.  This  pencil  point  is  pressed 
lightly  against  a  piece  of  paper  which  is  wrapped  about  a  cylinder  or  drum 
which  oscillates  upon  its  axis  in  unison  with  the  motion  of  the  piston  of 
the  engine.  This  is  accomplished  by  wrapping  a  cord  about  the  drum  and 
attaching  the  cord  to  a  pantograph  or  other  reducing  motion  which  is 
in  turn  attached  to  the  cross-head  of  the  engine  in  the  manner  shown  in 
Fig.  28.  The  cord  is  drawn  back  during  the  return  stroke  of  the  engine 
by  the  action  of  the  drum  spring.  The  motion  of  the  drum  will  then  be 
strictly  proportional  to  the  motion  of  the  piston,  and  the  distance  which  the 


ART.  130 


THE   THEORETICAL  INDICATOR  CARD 


103 


drum  revolves  during  any  portion  of  a  stroke  will  be  proportional  to  the 
volume  swept  by  the  piston  during  the  same  time.  Such  an  apparatus 
will  obviously  draw  the  PV  diagram  of  the  working  fluid  of  the  engine. 
Usually  an  indicator  card  is  taken  from  each  end  of  each  cylinder  of  an 
engine. 

130.  The  Theoretical  Indicator  Card.  The  indicator  card  which  is 
given  by  a  simple  engine  has  in  theory  the  form  shown  in  Fig.  29.  Assume 
that  this  card  represents  the  pressure-volume  diagram  of  the  head  end 
of  the  cylinder.  The  line  OX  is  "the  line  of  zero  pressure  and  the  line  OF, 
the  line  of  zero  volume,  the  two  forming  the  axes  of  the  diagram.  The 
abscissa  to  a  represents  the  volume  of  the  working  fluid  contained  in  the 
cylinder  when  the  piston  of  the  engine  is  at  the  extreme  left  of  its  stroke. 
This  volume  is  formed  by  the  space  included  between  the  face  of  the  pis- 


FIG.  29. — Theoretical  indicator  card. 

ton  and  the  head  of  the  cylinder,  the  volume  of  the  steam  and  exhaust 
ports,  and  the  small  volume  in  a  space  termed  the  counterbore.  The 
distance  between  the  face  of  the  piston  and  the  cylinder  head,  or  plate 
which  covers  the  end  of  the  cylinder,  is  termed  the  mechanical  clearance, 
and  varies  from  1/8  to  3/s  of  an  inch,  according  to  the  size  and  workman- 
ship of  the  engine.  In  order  to  avoid  forming  a  shoulder  in  the  cylinder 
where  the  piston  stops  at  the  end  of  its  travel,  the  cylinder  is  bored  out 
from  l/8  to  l/4  of  an  inch  larger  in  diameter  for  a  short  distance  at  either 
end.  The  space  so  formed  is  termed  the  counterbore.  The  sum  of  these 
three  volumes  taken  together  is  termed  the  clearance  volume  of  the 
engine  and  is  usually  expressed  as  a  per  cent  of  the  swept  volume  of  the 
cylinder.  The  swept  volume  of  the  cylinder  is  the  product  of  the  net 
piston  area  into  the  length  of  stroke.  The  area  of  the  piston  rod  must 
be  deducted  for  the  crank  end  of  the  cylinder.  The  volume  of  the  steam 
contained  in  the  cylinder  is  never,  of  course,  less  than  the  clearance  volume. 
As  the  piston  moves  to  the  right,  steam  follows  into  the  cylinder  from  the 


104 


THE  STEAM   ENGINE 


ART.  131 


boiler,  maintaining  the  pressure  constant,  the  increase  in  volume  mean- 
while being  strictly  proportional  to  the  distance  which  the  piston  travels. 
Point  b  represents  the  point  in  the  stroke,  and  the  total  volume  of  the  steam 
in  the  cylinder,  at  the  instant  that  the  inlet  valve  is  shut.  This  is 
termed  the  point  of  cut-off.  From  this  point,  as  the  volume  continues  to 
increase  with  the  advance  of  the  piston,  the  pressure  falls  off,  the  relation 
between  the  volume  and  pressure  being  expressed  very  nearly,  for  most 
engines,  by  the  equation 


in  which  K  is  a  constant  equal  to  the  product  of  the  absolute  pressure 
and  volume  at  the  point  of  cut-off.     The  line  be  is  then  very  nearly  a 


FIG.  30. — Actual  indicator  card. 

rectangular  hyperbola,  having  for  its  asymptotes  the  lines  0-X  and  0-Y. 
At  the  end  of  the  stroke  when  the  exhaust  valve  opens  the  pressure 
suddenly  drops  to  d,  the  ordinate  to  d  representing  the  pressure  in  the 
exhaust  pipe.  During  the  back  stroke,  the  pressure  continues  at  this 
value  until  the  point  e  is  reached,  when  the  exhaust  valve  closes  and 
compression  commences.  The  compression  of  the  mass  of  steam  con- 
fined within  the  volume  represented  by  the  abscissa  to  e  raises  the 
pressure  and  also  the  temperature  of  this  steam,  the  process  of  compres- 
sion being  represented  by  the  line  efy  which  is  also  like  the  expansion  line 
be,  very  nearly  a  rectangular  hyperbola. 

131.  The  Actual  Card.  The  actual  card  which  would  probably  be 
made  by  such  an  engine  would  be  represented  by  the  dotted  line  which 
falls  within  the  theoretical  card,  and  is  shown  separately  in  the  card  drawn 
in  Fig.  30.  On  this  card,  b  is  known  as  the  point  of  cut-off,  the  lino 
ab  is  known  as  the  steam  line,  the  line  be  is  known  as  the  expansion  line, 
c  is  known  as  the  point  of  release,  the  line  de  is  known  as  the  back-pressure 
line,  e  is  known  as  the  point  of  compression,  ef  is  known  as  the  com- 
pression line,  /  is  known  as  the  point  of  admission,  and  fe  is  known  as  the 


ART.  132  POWER  OF  THE  ENGINE  105 

admission  line.  The  steam  line  falls  below  the  theoretical  line,  since  a 
difference  in  pressure  is  necessary  to  force  the  steam  through  the  valve 
ports  at  a  velocity  which  usually  ranges  from  5000  to  10,000  feet  per  min- 
ute and  upward.  In  order  to  clear  the  cylinder  promptly,  it  is  necessary 
to  have  the  point  of  release  come  before  the  end  of  the  stroke,  as  otherwise 
too  much  work  would  be  required  during  the  back  stroke  to  force  the 
steam  out  of  the  cylinder.  The  back-pressure  line  will  be  above  the 
theoretical  back-pressure  line,  on  account  of  the  difference  in  pressure 
necessary  to  force  the  steam  through  the  exhaust  ports  at  a  velocity 
ranging  from  3000  to  7000  feet  per  minute.  Since  the  valves  open  and 
close  gradually  and  not  instantly,  the  card  will  have  rounded  corners  at 
the  points  of  cut-off,  release  and  compression. 

132.  Power  of  the  Engine.     As  in  the  case  of  any  other  pressure- 
volume  diagram  the  ordinates  of  the  indicator  card  are  proportional  to 
the  pressure  of  the  working  fluid,  the  abscissae  are  proportional  to  the 
change  in  volume,  and  the  area  is  proportional  to  the  work  done  by  the 
working  fluid.     It  is  usual  to  compute  the  power  of  the  engine  from  the 
area  of  its  indicator  card.     By  dividing  the  area  of  the  card  by  its  length 
(both  in  inches)  we  will  obtain  the  height  of  the  mean  ordinate   (also  in 
inches).     The  height  of  this  mean  ordinate  multipHed  by  the  "  scale  of 
the  spring  "  will  be  equal  to  the  average  absolute  pressure  in  pounds  per 
square  inch   on   the  piston  throughout  the  working  stroke    minus  the 
average  pressure  during  the  back  stroke,  a  quantity  which  is  termed  the 
mean  effective  pressure.     If  we  multiply  the  mean  effective  pressure  by  the 
net  area  of  the  piston  and  that  by  the  length  of  stroke,  we  will  have  the 
work  done  in  foot-pounds  per  stroke.     Multiplying   by  the  number  of 
strokes  per  minute,  and  dividing  by  33,000,  we  obtain  the  indicated  horse 
power  of  the  engine,  or  the  rate  at  which  heat  energy  is  transformed  into 
work  in  the  cylinder  by  the  action  of  the  working  fluid.     In  the  case  of  a 
double-acting  engine,  it  is  necessary,  when  the  mean  effective  pressure 
and  the  net  piston  area  of  the  two  sides  of  the  piston  are  materially 
different,  to  calculate  the  power  for  each  end  of  the  cylinder  separately, 
and  to  add  to  the  results. 

133.  Methods  of  Governing.     In  order  that  a  steam  engine  shall  be  a 
useful  source  of  power,  it  is  necessary  that  its  speed  shall  be  very  nearly 
constant.     This  means  that  the  power  generated  by  the  expanding  steam 
within  the  cylinder  shall  be  equal  to  the  friction  losses  in  the  engine  plus 
the  power  required  by  the    machinery    which  the  engine  drives.     In 
order  to  secure  this    continuous    adjustment    of  the    power  developed 
within  the  cylinder  to  the  varying  needs  of  external  machinery,  it  is 
necessary  to  control  the  quantity  of  steam  admitted  to  the  cylinder 
during  each  stroke.     We  may  accomplish  this  in  two  ways.     We  may, 
by  causing  the  steam  to  pass  through  a  restricted  opening,  reduce  the 


106 


THE   STEAM   ENGINE 


ART.  134 


FIG.  31.— Theoretical  cards  from  a  throttle 
governed  engine. 


pressure  at  which  a  given  volume  of  steam  is  admitted  to  the  cylinder.     Or 
we  may,  by  closing  the  inlet  valve  earlier  in  the  stroke,  reduce  the  volume 
of  steam  admitted  at  the  cylinder  at  boiler  pressure.     The  first  method 
of  controlling  the  speed  of  the  engine  is  known  as  throttle  governing. 
The  second  method  of  controlling  the  speed  of  the  engine  is  known  as  cut- 
off governing.      The   effect 
of  throttle  governing  upon 
the  indicator  card  given  by 
a  steam  engine  is  shown  in 
Fig.  31.     The  heavy  outline 
shows  the  form  of  the  card 
given  by  the  engine  when 
the    throttle   valve,    which 
controls  the  flow  of  steam 
to    the    cylinder,    is    wide 
open.      The   light   outlines 
show  the  theoretical   form 
of  the  steam  and  expansion 

lines  of  the  card  when  the  throttle  valve  is  closed  to  a  greater  or  less 
degree.  In  the  case  of  an  actual  engine,  the  cards  would  not  be  of  the 
form  shown  in  Fig.  31,  but  rather  of  the  form  shown  in  Fig.  32.  Since 
the  speed  of  the  piston  is  greatest  at  the  middle  of  the  stroke,  the  effect 
of  the  throttle  valve  in  reducing  the  pressure  of  the  steam  is  greatest 
at  that  point;  consequently, 
the  steam  lines  have  in  prac- 
tice the  form  shown  in  Fig. 
32,  rather  than  that  shown  in 
Fig.  31. 

134.  The  Throttling  Gov- 
ernor. The  construction  and 
operation  of  a  throttling  gov- 
ernor may  be  understood  by 
reference  to  Fig.  33.  In  the 
figure,  a  is  a  steam  pipe  sup- 
plying steam  to  the  engine  to 
be  governed  and  B  is  a 

balanced  valve  in  this  pipe.  When  the  valve  is  at  its  highest  position, 
the  pipe  is  wide  open  and  the  steam  can  flow  freely  from  pipe  a  into 
the  steam  chest  C  by  the  route  shown  by  the  arrow.  When,  however, 
the  valve  is  forced  down,  the  area  of  the  opening  through  which  the  steam 
may  flow  is  very  greatly  diminished,  so  that  a  large  difference  in  pressure 
is  required  to  cause  the  quantity  of  steam  taken  by  the  engine  to  flow 
through  the  restricted  opening.  Since  this  difference  in  pressure  is  used 


FIG.  32. — Actual  cards  from  a  throttle 
governed  engine. 


ART.  135 


CUT-OFF  GOVERNING 


107 


in  forcing  the  steam  through  the  throttle  valve,  it  is  not  available  to  drive 

the  piston  of  the  engine,  and  the  power  of  the  engine  is  therefore  reduced. 

The  valve  B  is  attached  to  the  rod  or  stem  dy  which  protrudes  through 

the    stuffing-box    e.       This    rod    is    forced 

upward    by    the    helical    spring  /.      Two 

weights  or   balls,   gg,   are   pivoted   to    the 

arms  hh,  which  are   caused  to  revolve  by 

the  gearing  shown.     The  centrifugal  force 

so   developed   causes   the    weights    to    fly 

outward,   and  to    draw    down    the    valve 

stem  against  the  resistance  of  the  spring. 

As  the  engine  speeds   up,  centrifugal   force 

throws  the  balls  still  further  out,  drawing 

down  the  stem,   and  closing  the  throttle 

valve.     When  the   engine  slows  down,  the 

spring    forces    the   stem   up,    opening   the 

throttle    valve.     Any    increase    above    the 

normal   speed  will  thus   reduce  the  steam 

supply  to  the   engine,  while    any  decrease 

below  the  normal  speed  will  increase  this 

steam  supply.      The  governor  is  operated 

by  means  of  a  belt  or  other  form  of  gearing 

connecting  it  with  the  shaft  of  the  engine. 

135.  Cut-off  Governing.     The  variation  in  the  form  of  card  given  by 

an  engine  governed  by  means  of  a  variable  cut-off  governor  is  shown  in 

Fig.  34.      By  shortening   the    cut-off,  the  quantity  of  steam  admitted, 

the  area  of  the  card,  and  the 
power  of  the  engine  are  all 
reduced.  The  heavy  outline 
shows  the  form  of  card  given 
at  normal  load.  The  light 
outlines  show  the  form  of  card 
at  light  load,  while  the  dotted 
line  shows  the  forms  of  card 
when  the.  load  reaches  the 
maximum. 

136.  Comparison  of  Meth- 
ods of  Governing.  An  in- 
spection of  Fig.  35  will  show 

that    cut-off    governing     is    preferable     to     throttle    governing,     from 

the  standpoint  of    steam    economy.      In  the  figure  the  heavy  outlines 

show  the  card  given  by  both  a  throttle-governed  engine,  and  a  cut-off 

governed  engine.,   at  full  load.     Both  engines  take   the   same  quantity 


JTIG-  33. 


FIG.  34. — Actual  cards  from  a  cut-off 
governed  engine. 


108 


THE  STEAM   ENGINE 


ART.  137 


of  steam,  and  perform  the  same  quantity  of  work,  and  are  there- 
fore equally  efficient.  The  light  outlines  bound  the  cards  given  by  the 
same  engines  at  a  lower  load.  The  engines,  as  before,  take  the  same 
quantity  of  steam.  However,  the  cut-off  governed  engine  does  the  work 
represented  by  the  area  abode,  while  the  throttle-governed  engine  does 
the  work  represented  by  the  area  fgcde.  The  latter  is  less  than  the  former 
by  the  shaded  area,  and  the  efficiency  of  the  throttle-governed  engine 
is  correspondingly  less  than  that  of  the  cut-off  governed  engine.  Con- 
sequently, we  find  that  practically  all  first-class  modern  engines  are 
governed  by  a  variable  cut  off,  and  not  by  throttling. 

The  mechanism  used  for  producing  a  variable  cut-off  is  usually  much 
more  costly  and  complicated  than  that  used  in  throttle  governing.  The 
general  types  of  valves  used  for  this  purpose  and  the  mechanisms  employed 
for  moving  them  will  be  discussed  in  the  remaining  paragraphs  of  the 


FIG.  35. — Comparison  of  throttle  and  cut-off  governing. 

present  chapter,  in  connection  with  the  descriptions  of  different  types 
of  engines  now  in  use. 

137.  The  Common  Slide  Valve.  The  form  of  valve  most  commonly 
employed  in  the  smaller  sizes  of  steam  engines  is  known  as  the  slide 
valve.  The  simplest  form  of  the  slide  valve  is  that  shown  in  section  in 
Fig.  36,  and  known  as  the  D  valve  on  account  of  its  shape.  In  this 
figure,  which  is  a  longitudinal  section  through  the  cylinder  and  steam 
chest,  the  valve  is  the  blackened  part  marked  V.  The  valve  covers  the 
ports  P  and  P'  leading  to  the  head  and  crank  end  of  the  cylinder.  Steam 
enters  the  valve  chest  from  the  steam  pipe,  and  as  the  valve  moves  to  the 
right  into  the  position  shown,  the  port  Pis  uncovered,  allowing  the  steam 
to  flow  into  the  cylinder  and  propel  the  piston  to  the  right.  At  the  same 
time  the  steam  contained  in  the  crank  end  of  the  cylinder  escapes  through 
the  port  P,  into  the  exhaust  port  E,  by  the  route  shown  by  the  arrow. 
The  valve  is  caused  to  move  back  and  forth  by  the  action  of  an  eccentric 


ART.  137 


THE  COMMON   SLIDE   VALVE 


109 


on  the  engine  shaft.  The  eccentric  is  a  disk  whose  diameter  is  much 
greater  than  that  of  the  shaft  to  which  it  is  attached,  and  which  acts  in 
the  same  manner  as  a  crank,  since  its  center  does  not  coincide  with  the 
center  of  the  shaft.  As  the  piston  continues  to  move  to  the  right,  the 
valve  begins  to  move  to  the  left,  finally  shutting  off  the  supply  of 
steam,  and  expansion  begins.  When  the  piston  approaches  the  end  of 
its  stroke,  the  valve  still  moving  to  the  left  shuts  off  the  port  P'  from  the 


FIG.  36.— The  D  valve  and  ports. 

exhaust  port,  and  compression  begins  in  the  crank  end  of  the  cylinder. 
When  the  piston  reaches  the  end  of  its  stroke,  the  valve  will  have  moved 
to  the  left  sufficiently  to  uncover  the  port  P'  to  the  steam  in  the  valve 
chest,  and  the  port  P  to  the  exhaust  port.  During  the  back  stroke  of  the 
engine,  the  same  series  of  events  occurs,  except  that  the  opposite  end  of 
the  cylinder  is  involved  in  each  case. 


FIG.  37. — Steam  and  exhaust  lap. 

In  order  to  accomplish  these  results,  it  will  be  seen  that  it  is  necessary 
when  the  valve  is  in  its  central  position,  for  the  two  ends  of  the  valve  to 
extend  some  distance  beyond  the  inlet  edges  (i  and  ir)  of  the  ports,  as  is 
shown  in  Fig.  37.  The  distance  A  is  known  as  the  steam  lap  of  the  valve, 
and  may  be  the  same  or  may  be  different  for  each  end  of  the  cylinder. 
It  is  usual  for  the  exhaust  edges  of  the  ports  to  coincide  with  the  exhaust 
edges  of  the  valve,  when  the  valve  is  in  the  central  position.  Sometimes 
the  ports  are  slightly  uncovered  as  at  E' ,  arid  sometimes  they  are  cov- 


110  THE  STEAM   ENGINE  ART.  138 

ered  as  at  E,  with  the  valve  in  this  position.  The  distance  from  the 
exhaust  edge  of  the  port  to  the  exhaust  edge  of  the  valve  is  termed 
negative  exhaust  lap  in  the  first  case,  and  positive  exhaust  lap  in  the 
second.  The  distance  which  the  valve  moves  in  going  from. one  of  its 
extreme  positions  to  the  other  is  called  the  travel  of  the  valve,  and  is 
twice  the  eccentricity  or  throw  of  the  eccentric. 

By  changing  the  travel  of  the  valve  (i.e.,  the  eccentricity  of  the  eccen- 
tric) and  the  angular  distance  between  the  eccentric  and  the  crank,  it 
is  possible  to  change  the  point  in  the  stroke  at  which  cut-off  occurs. 
Such  a  change  will  also  affect  the  point  in  the  stroke  at  which  admission, 
exhaust,  and  compression  begins,  but  these  changes  will  not  be  as  great 
as  the  change  in  the  time  of  cut-off.  If  the  eccentric  be  connected  to  a 
governing  mechanism  which  will  automatically  adjust  its  eccentricity 
and  position  in  accordance  with  the  power  required  of  the  engine,  we 
may  effect  cut-off  governing  by  the  slide  valve.  An  engine  so  governed 
is  usually  termed  an  automatic  engine. 

138.  Defects  of  the  Common  Slide  Valve.  The  D  valve  has  the 
following  defects:  First,  on  account  of  the  rather  long  and  crooked 
steam  passages,  the  clearance  volume  of  the  engine  will  be  excessive. 
The  result,  as  will  appear  in  the  next  chapter  is  a  considerable  waste  of 
steam.  Second,  the  area  of  the  surfaces  enclosing  the  clearance  space 
will  be  very  large,  which  will  be  shown  in  Chapter  X  to  result  in  a  great 
waste  of  steam.  Third,  the  valve  opens  and  closes  gradually  instead 
of  promptly,  and  the  card  given  by  the  engine  shows  to  an  excessive 
degree  the  effects  of  wire  drawing.  As  a  result,  the  power  given  by  the 
engine  for  a  given  weight  of  steam  is  considerably  less  than  if  the  valves 
opened  and  closed  promptly.  Fourth,  the  pressure  of  the  steam  on  the 
back  of  the  valve  forces  it  down  upon  its  seat,  thus  causing  it  to  wear 
excessively  and  to  require  a  considerable  amount  of  power  to  drive  it. 
Fifth,  when  the  plain  slide  valve  is  used  in  an  automatic  engine^  on  account 
of  the  shifting  of  the  points  of  compression  and  release,  the  card  is  greatly 
distorted  from  its  proper  form,  except  at  some  particular  load,  which 
reduces  the  power  obtained  from  the  engine  for  a  given  steam  consump- 
tion. In  order  to  overcome  these  several  disadvantages,  a  great  many 
types  of  valves  have  been  invented. 

The  excessive  clearance  and  area  of  clearance  surfaces  may  be  reduced 
by  lengthening  the  valve,  so  that  the  ports  may  be  made  short  and  direct. 
By  doing  so,  however,  we  greatly  increase  the  total  pressure  of  the  steam 
upon  the  valve,  and  therefore  the  friction  and  wear.  In  order  to  reduce 
this  source  of  loss,  the  valve  is  usually,  in  the  better  class  of  engines, 
made  of  such  a  form  that  the  pressure  of  the  steam  is  balanced.  Such 
a  valve  is  termed  a  balanced  valve.  In  order  that  the  valve  shall  open 
and  close  promptly,  it  is  usual  in  all  but  the  smallest  engines  to  use  what 


ART.  139 


BALANCED   SLIDE   VALVES 


111 


is  termed  a  double-ported  valve ;  that  is  one  which  will  admit  the  steam  at 
two  edges  instead  of  at  one  edge  only.  In  order  to  avoid  the  shifting 
of  the  points  of  release  and  compression,  as  the  load  upon  an  automatic 
engine  varies,  an  auxiliary  valve,  whose  purpose  it  is  to  regulate  the  point 
of  cut-off,  is  sometimes  employed.  Such  a  valve  is  called  a  riding  cut-off 
valve. 

139.  Balanced  Slide  Valves.     The  simplest  method  of  balancing  the 
slide  valve  is  to  use  a  valve  which  is  cylindrical  in  form,  instead  of  a  flat 

valve.  Such  a  valve  is  shown  in 
Fig.  38.  The  steam  is  admitted 
at  one  end  of  the  valve  chest, 
and  since  the  valve  is  hollow,  it 
can  pass  from  one  end  to  the 
other.  The  action  of  the  valve 
may  be  readily  inferred  from  the 
FIG.  38.  drawing,  and  it  differs  in  no  way 

from  the  action   of    the    D    valve. 

A  second  method  of  balancing  the  slide  valve  is  that  shown  in  Fig.  39, 
in  which  the  valve  is  a  perfectly  flat  rectangular  plate  covered  by  a  second 
plate  having  in  it  slight  recesses  exactly  opposite  to  the  steam  and  exhaust 
ports,  and  connected  to  them  by  passages  through  the  valve  itself.  Since 
the  pressure  on  both  sides  of  this  valve  is  exactly  the  same,  the  friction 
resisting  its  motion  is  negligible.  The  objection  to  both  these  methods 
of  balancing  slide  valves  is  that  the  valves  leak,  about  25  per  cent  of  the 


FIG.  39. — Straight-Line  valve. 


steam  consumption  of  engines  using  these  types  of  valves  being  due  to 
such  leakage.  Various  other  methods  of  balancing  slide  valves  are  in 
use,  and  the  reader  is  referred  to  Halsey's  "  Slide  Valve  Gears  "  for  a 
more  complete  treatment  of  the  subject. 

140.  Multi-ported  Slide  Valves.  The  simplest  form  of  the  double- 
ported  valve  is  the  Allen  valve  illustrated  in  Fig.  40.  The  port  cored 
in  the  body  of  the  valve,  permits  the  steam  to  pass  into  the  steam  ports 
by  the  two  routes  indicated  by  the  arrows.  A  displacement  of  the 
valve  of  any  given  small  amount  to  the  right  of  the  position  shown  will 


112 


THE   STEAM   ENGINE 


AKT.  141 


increase  the   width    of   the   port   opening  by  twice  the    amount  of  the 
displacement. 

A  method  of  double-porting  a  balanced  slide  valve  is  illustrated  in 
Fig.  39,  which  represents  the  Straight-Line  valve  as  applied  to  the 
Straight-Line  engine.  The  path  of  the  steam  through  the  double  ports 
may  be  inferred  from  the  arrows,  which  show  that  the  steam  is  admitted 
at  two  edges  at  the  same  time.  Double  porting  the  slide  valve  serves 


FIG.  40. — Allen  double  ported  valve. 

to  reduce  the  friction  of  the  valve  for  a  given  port  opening,  and  therefore 
the  friction  and  wear.  The  same  rapidity  of  port  opening  may  of  course 
be  obtained  by  using  a  common  D  valve  with  twice  the  travel,  but  it 
is  not  always  advisable  to  give  a  valve  such  an  amount  of  travel. 

141.  Riding  Cut-offs.     The  simplest  form  of  the  riding  cut-off  valve 
is  illustrated  in  Fig.  41,  and  is  known  as  the  Meyer  valve.     The  main 


FIG.  41. — Meyer  riding  cut-off  valve. 

valve  acts  as  a  seat  upon  which  the  cut-off  valve  slides,  the  cut-off 
valve  being  driven  by  a  separate  eccentric.  The  cut-off  valve  is  formed 
in  two  parts,  as  shown,  in  order  that  the  point  of  cut-off  may  be 
altered  by  altering  the  distance  between  them.  This  is  accomplished 
by  threading  the  two  halves  of  the  valve  to  the  valve  stem  with  a 
right-  and  left-handed  thread  in  order  that  by  turning  the  valve  stem, 
they  may  be  made  to  approach  or  recede.  This  type  of  valve  is  much 
used  in  slow-moving  engines  operated  without  governors,  such  as  air 
compressors  and  pumping  engines.  It  is  not,  however,  as  satisfactory 


ART.  142  APPLICATION   OF  SLIDE-VALVE  ENGINES  113 

as  other  forms  of  riding  cut-off,  such  for  instance  as  the  Buckeye  valve, 
which  may  be  found  described  in  Halsey's  book,  to  which  reference  has 
already  been  made. 

142.  Application  of  Slide-valve  Engines.  The  slide-valve  engine  is 
usually  built  in  sizes  up  to  300  or  400  horse-power  for  stationary  service, 
and  in  larger  powers  when  compact  engines  of  high  speed  of  rotation  are 
desired.  It  is  not  as  economical  in  the  use  of  steam  as  are  other  types 
of  engines,  and  is  being  steadily  displaced  by  the  steam  turbine  and  by  the 
four-valve  engine.  In  stationary  service,  in  the  smallest  sizes,  a  fixed 
eccentric  and  throttle  governor  are  commonly  used.  In  the  larger  sizes, 
the  valve  is  made  double-ported  and  balanced  and  an  automatic  shaft 
governor  is  used.  In  spite  of  the  greater  economy  which  it  offers  the 
riding  cut-off  is  seldom  employed. 

The  slide-valve  engine  finds  its  principal  application  in  high  powers  in 
connection  with  locomotive  and  the  marine  engines.  The  valve  employed 
for  high  steam  pressures  is  usually  a  double-ported  piston  valve,  while 
for  low  pressures  a  double-ported  balanced  flat  valve  is  usual.  Neither 
locomotives  nor  marine  engines  are  provided  with  governors,  and  the 
eccentrics  are  fixed.  However,  the  point  of  cut-off  and  the  power  of  the 
engine,  in  both  cases,  is  controlled  by  means  of  an  arrangement  termed 
a  link  motion.  The  Stevenson  link 
motion  was  formerly  employed 
almost  exclusively,  but  other  forms, 
notably  the  Waelchert  valve  gear, 
have  been  found  more  suitable  for 
very  large  powers  and  high  steam 
pressures.  These  valve  gears  are 
manually  controlled,  the  engineer 
determining  the  speed  and  power 
of  the  engine  by  the  position  of 
the  link  motion.  Although  slide 
valves  have  been  used  exclusively 
in  locomotive  and  marine  engine 
service,  there  is  just  as  good  reason  FIG.  42. —  Portable  engine  and  boiler, 
to  believe  that  the  employment  of  Engine  with  throttling  governor, 

other  types  of  valve  motion  would 

give  superior  results  in  this  class  of  service  as  in  any  other.  It  is  reason- 
able to  suppose,  therefore,  that  four-valve  engines  will  be  eventually 
employed  in  locomotive  and  marine  service,  since  they  are  giving  most 
excellent  results  in  stationary  service. 

In  Fig.  42  may  be  seen  an  illustration  of  a  plain  slide-valve  engine 
with  a  throttle  governor  mounted  upon  a  portable  boiler.  This  is  a  type 
of  power  plant  often  employed  in  agricultural  service.  In  Fig.  43 


114 


THE   STEAM   ENGINE 


ART.  442 


is  an  illustration  of  a  single -cylinder  high-speed  automatic  engine  with  a 
double-ported  balanced  valve,  such  as  is  usually  employed  in  stationary 
service  when  the  power  required  is  small,  and  the  engine  runs  non-con- 
densing. This  engine  is  equipped  with  a  shaft  governor.  Fig.  44  is 
an  illustration  of  the  cylinder  and  drive  wheels  of  a  locomotive  equipped 
with  a  Waelschert  valve  gear. 


FIG.  43. — High  speed  simple  engine  with  "automatic"  cut-off  governor. 

A  locomotive  of  this  type  has  two  cylinders  of  largesize,  uses  steam  of 
very  high  pressure,  and  operates  at  very  high  speed,  developing  from 
700  to  1200  horse-power  in  each  cylinder.  On  account  of  the  large 
number  of  locomotives  in  service,  and  their  very  great  aggregate  power, 
the  matter  of  locomotive  engine  efficiency  is  of  immense  practical 


FIG.  44. — Cylinder  and  drive  wheels  of  a  locomotive  with  Waelschert  gear. 

importance.  In  Fig.  45  may  be  seen  an  illustration  of  a  triple-expan- 
sion, four-cylinder  marine  engine,  such  as  is  commonly  built  for  naval 
service.  These  engines  are  of  immense  power  for  their  size  and  weight 
and  run  at  very  high  speed.  The  high-pressure  cylinders  are  equipped 
with  piston  valves  and  the  low-pressure  cylinders  with  balanced  flat 


ABT.  442 


APPLICATION  OF  SLIDE-VALVE  ENGINES 


115 


116  THE  STEAM   ENGINE  ART.  143 

valves,  all  operated  by  Stevenson  link  motion.  This  link  motion  is  not 
moved  directly  by  the  engineer,  as  is  the  case  with  the  locomotive,  but 
is  operated  by  means  of  a  steam  cylinder,  which  is  controlled  by  the 
engineer,  the  links  being  too  large  and  heavy  to  be  manually  operated. 
The  variety  of  slide  valves  in  actual  use  is  so  numerous  and  the  methods 
of  designing  them  are  such  as  to  forbid  an  adequate  treatment  of  the 
subject  in  a  work  of  this  kind.  For  a  full  treatment  of  American  slide 
valves  and  the  best  methods  of  designing  them  the  reader  is  referred  to 
Halsey's  "  Treatise  on  Slide  Valve  Gears." 

143.  The  Corliss   Engine.      The  Corliss  engine  makes  use  of  valves 
of  the  form  shown  in  Fig.  26,  in  order  to  avoid  the  disadvantage  accom- 
panying the  use  of  slide  valves.     By  the  use  of  the  Corliss  valve  the  ports 
may  be  made  short  and  direct.     The  clearance  volume    and    clearance 
area  are  reduced  to  a  minimum,  which  results  in  greatly  increasing  the 
steam  economy.     In  addition  the  mechanism  which  operates  the  valves 
is  so  arranged  that  the  valves  are  caused  to  open  and  close  promptly, 
thus  avoiding  a  loss  of  power  from  wire  drawing.     The  closing  of  the 
inlet  valve  at  the  point  of  cut-off  is  effected  in  such  a  way  as  to  leave 
the   points   of   admission,   release,    and   compression   unchanged,   which 
permits  them  always  to  occur  at  the  proper  point  in  the  stroke. 

144.  The  Corliss  Valve  Motion.     The  mechanism  employed  for  operat- 
ing the  valves  of   a  Corliss   engine  is   illustrated  in  Fig.  46.     W  is  the 
wrist  plate,  which  turns  upon  a  pin  fastened  to  the  side  of  the  cylinder. 
It  is  operated  by  the  reach  rod  R,  which  is  pinned  at  the  other  end  to  the 
rocker  arm  A,  which  in  turn  is  operated  by  the  eccentric  rod,  the  other  end 
of  which  is  fastened  to  the  eccentric  strap,  which  embraces  the  eccentric 
E.     Attached  to  the  wrist  plate  are  four  rods  termed  valve   rods  leading 
to  the    levers   which  operate  the  four  valves  of  the  engine.     The  rods 
B  and  E'  are  pinned  to  the  arms  C  and  C',  which  in  turn  are  keyed  to 
short  shafts  termed  valve  stems  which  serve  to  rotate  the  exhaust  valves. 
As  the  wrist  plate  is  vibrated  by  the  action  of  the  eccentric,  the  valves 
are  caused  to  move,  opening  and  closing  at  the  proper  time.     The  action 
of  the  wrist  plate  is  such  that  at  the  end  of  their  travel,  while  they  are 
closed,  the  valves  are  practically  stationary,  as  will  be  the  case  with  the 
left  end  or  head  end  exhaust  valve,  when  the  wrist  plate  is  in  the  posi- 
tion shown  in  Fig.  47.     This  allows  of   a  rapid   opening    of  the  valve 
without  an  excessive  valve  travel. 

The  valve  rod  D  is  pinned  to  the  bell  crank,  or  latch  arm  F  in 
Fig.  48,  which  turns  freely  upon  the  inlet-valve  stem.  Pinned  to  the 
latch  arm  is  a  latch  which  when  the  arm  is  in  the  position  shown,  catches 
a  block  affixed  to  the  inlet-valve  arm  G,  and  as  the  latch  arm  is  drawn 
to  the  right  the  valve  arm  is  caused  to  rotate,  opening  the  valve.  When 
this  rotation  has  proceeded  for  a  sufficient  length  of  time  to  allow  the 


ART.  143 


THE  CORLISS  ENGINE 


117 


118 


THE  STEAM   ENGINE 


ART.  144 


desired  cut-off,  the  latch  strikes  the  cam  H  (whose  position  is  fixed  by 
the  governor)  which  pushes  up  the  latch  and  releases  the  block.  The  rod 
/,  pinned  to  the  valve  arm,  leads  to  ihe  dashpot  /.  Within  this  dashpot 
is  a  piston,  the  raising  of  which  creates  a  suction  which  returns  the  valve 


FIG.  47.— Corliss  valve  motion  with  wrist  plate  in  extreme  position. 

to  the  closed  position  the  instant  the  cam  causes  the  latch  to  release 
the  block.  This  piston  is  so  arranged  that  just  before  it  strikes  the  bot- 
tom of  the  cylinder  it  compresses  a  quantity  of  air,  which  prevents  the 
violent  blow  or  jar  which  would  otherwise  result.  By  this  device,  a 


FIG.  48. — Inlet  valve  gear. 

very  rapid  closing  of  the  ports  is  secured.  A  still  more  rapid  opening 
and  closing  of  the  ports  of  a  Corliss  engine  may  be  secured  by  the  use 
of  double-ported  valves,  such  as  are  shown  in  section  in  Fig.  49. 

It  is  often  desirable  to  use  two  eccentrics,  operating  two  wrist  plates, 


ART.  145 


THE   FOUR-VALVE  ENGINE 


119 


one  of  which   moves   the    exhaust 

valves    and    the    other    the    inlet 

valves.     This  permits    of   a   much 

later  cut-off  than  is  possible  when 

one  eccentric  is  used.  When  Cor- 
liss engines  are  required  for  rail- 
way or  other  service  where  the 

variation  in  load   is   extreme,  this 

type  of  engine  is  preferred.     When 

the    load    is   fairly    constant,    the 

single  eccentric   type   is  equally  as 

satisfactory  and  economical. 

145.  The     Four- valve    Engine. 

A    type    of   engine   known   as    the 

four-valve     automatic      engine     is 

rapidly     coming     into     favor     for 

smaller   powers  (i.e.,  up  to  300  to 

500    horse-power).      The    exhaust 

valves  of  this  type  of  engine   are 

operated  in  the  same  way  as  are 

the    exhaust    valves    of    a    Corliss 

engine.     The  inlet  valves,  however, 

are     operated     directly    from    the 

inlet- valve   wrist   plate,   the   inlet  - 

valve    rods    being    pinned    to    the 

valve    arms,   which    are    keyed   to 

the  valve    stems.     The    cut-off    is 

effected    by    changing    the   throw 

and  angular  position  of  the  eccentric 

which  operates  the   inlet-valve  wrist   plate.      All   of  the  advantages  of 

the    Corliss    engine    are  realized    in   the    four- valve    automatic  ^engine, 

excepting  the  prompt',  closing 
of  the  inlet  valve  at  cut-off. 
The  form  of  card  given  by  the 
four-valve  engine  is  shown  in 
Fig.  50.  There  is  no  material 
difference  between  the  steam 
economy  of  the  four-valve  auto- 
matic engine  and  of  the  Cor- 
liss engine,  but  the  four- valve 
automatic,  since  it  may  be 
operated  at  higher  speeds,  is 


Exhaust  Valve 

FIG.  49.— Sections  through  Corliss  inlet 
and  exhaust  valves. 


FIG.  50. — Typical  card  from  a  four  valve 
engine. 


the  cheaper  type,  and  since  it 


120 


THE   STEAM   ENGINE 


ART.  461 


is  simpler,  it  is  less  likely  to  get  out  of  order.  The  governor  employed 
with  the  four-valve  automatic  engine  is  a  shaft  governor,  while  that 
employed  with  the  Corliss  engine  is  usually  a  fly-ball  governor,  such  as 
is  shown  in  Fig.  46. 

146.  Gridiron  Valves.     Another  type  of  valve  which  is  used  in  a  good 
many  makes  of  steam  engines  is  the  gridiron  valve,  which  is  illustrated  in 


FIG.  51. — Section  through  a  gridiron  valve. 

Fig.  51.  The  seat  upon  which  this  valve  rests  contains  a  series  of  parallel 
slots  separated  by  metal  bridges  somewhat  wider  than  the  slots,  while 
the  valve  itself  contains  a  similar  set  of  slots.  When  the  slots  are  opposite 
one  another,  the  steam  passes  through  the  valve.  When,  however,  the 


FIG.  52. — Mclntosh-Seymour  cross  compound  engine. 

bridges  of  the  valve  cover  the  slots  in  the  seat,  as  shown  in  the  drawing, 
steam  cannot  pass  through.  Various  types  of  mechanism  are  employed  for 
operating  gridiron  valves.  The  Mclntosh-Seymour  engine,  illustrated 
in  Fig.  52,  is  fitted  with  gridiron  valves,  and  is  an  example  of  a  type  of 
mechanism  often  employed  for  operating  them.  The  engine  equipped 
with  gridiron  valves  is  equally  as  economical  as  the  Corliss  engine,  and 
was  formerly  equally  as  cheap  to  build.  Changes  in  shop  methods  have 


ART.  147 


POPPET-VALVE   ENGINES 


121 


resulted  in  making  the  Corliss  type  the  cheaper  one  to  build,  so  that  most 
large  engines  are  now  equipped  with  Corliss  valves. 

147.  Poppet-valve  Engines.  A  type  of  valve  very  much  employed  in 
European  practice  is  known 
as  the  poppet  valve.  The 
poppet  valve  is  of  two  forms, 
the  one  shown  in  Fig.  53 
being  known  as  a  plain  pop- 
pet valve  and  that  shown  in 
Fig.  54  as  a  balanced  valve. 
In  steam  engine  work  the 
balanced  poppet  valve  is 
usually  employed.  Poppet- 
valve  engines  are  usually 
four-valve  engines,  although 
poppet  valves  are  sometimes  • 
employed  in  pairs  and  some- 
times in  connection  with 
Corliss  or  other  types  of 


FIG.  53. — Plain  poppet  exhaust  valve. 


valves.       Balanced    poppet 
valves    have   the    disadvan- 
tages   of  requiring    a  large   clearance  volume  and  of  exposing  a  con- 
siderable clearance  area  to  the  action  of  the  steam.     They  are,  however, 

better  adapted  to  the  use 
of  superheated  steam, 
and  are  tighter  than  are 
other  forms  of  valves, 
and  are  therefore  much 
used  in  connection  with 
superheated  steam.  A 
tripple-expansion  pump- 
ing engine  in  which  pop- 
pet valves  are  used  for 
the  exhaust  valves  of 
the  intermediate  cylin- 
der, and  the  inlet  and 
exhaust  valves  of  the 
low-pressure  cylinder,  is 
illustrated  in  Fig.  55.  In 
FIG.  54. — Balanced  or  double-beat  poppet  inlet  valve,  a  poppet-valve  engine, 

as  in  the  Corliss  engine, 

cut-off  is  effected  by  releasing  the  valve  from  the  control  of  the  opening 
mechanism,  and  allowing  it  to  close  quickly  by  the  action  of  a  dashpot. 


122 


THE  STEAM   ENGINE 


ART.  147 


FIG.  55.— Vertical  triple-expansion  pumping  engine. 


ART.  148  SPECIAL  TYPES  OF  ENGINES  123 

Excellent  results  in  steam  economy  have  been  obtained  from  poppet-valve 
engines,  but  these  results  are  to  be  credited  rather  to  the  fact  that  highly 
superheated  steam  was  employed  than  to  any  excellence  inherent  in  the 
type  of  valve.  The  use  of  plain  poppet  valves  in  the  low-pressure  cylinder 
of  a  steam  engine  permits  of  greatly  reducing  the  clearance  volume  and 
the  resulting  loss.  By  employing  this  type  of  valve,  engines  have  been 
designed  in  which  the  clearance  volume  was  only  0.35  per  cent  of 
the  swept  volume.  In  such  a  case,  the  clearance  loss  is  exceedingly 
small. 

148.  Rotary  Engines.      Many  attempts  have  been  made  to  so  design 
the  steam  engine  as  to  avoid  the  use  of  a  reciprocating  piston  and  cross- 
head,  applying  the  expansive  pressure  of  the  steam  directly  to  rotating 
parts.     Engines   operating   on   this   principle   are   usually   called   rotary 
steam  engines.     The   rotary  steam  engine   has    not   proved   successful, 
for  two  reasons.     First,  the  form  of  cycle  which  must  be  employed  with 
any  of  the  possible  mechanisms  is  wasteful  of  steam,  and  secondly,  the 
friction  and  wear  of  the  parts  are  excessive.    Since  the  mechanical  efficiency 
of  a  well-designed  reciprocating  engine  is  high,  there  is  no  practical  reason 
for  the  use  of  a  rotary  engine  except  a  possible  reduction  in  the  volume 
and  weight  of  the  engine.      This  advantage,   however,  is  outweighed  in 
all  cases  by  the  larger  steam  consumption  and  more  rapid  deterioration 
of   engines  of  this' type. 

149.  Special  Forms  of  the  Steam  Engine.     Many  special  forms  of 
the  steam  engine  are  employed  for  special  service.     The  steam  himmer, 
for  instance,  is  a  special  form  of  an  engine  with  manually  operated  valves. 
Direct-acting  steam  pumps,  the  locomotive  i  ir  pump,  the  steam  steering- 
engine,  the  pulsometer,  the  steam  drill  £nd  other  types  are  examples  of 
highly  specialized  types  of  steam  engines,  adapted  to  work  under  peculiar 
conditions,  or  to  perform  unusual  kinds  of  service.     Such  engines  are 
usually  of  peculiar  construction  mechanically,  and  are  almost  invariably 
very  wasteful  in  their  use  of  steam,  and  are  employed  only  because  they 
offer  superior  advantages  in  the  matter  of  cheapness,  simplicity,  adaptabil- 
ity, or  ruggedness  of  mechanism. 


PROBLEMS 

1.  An  engine  takes  steam  of  98  per  cent  quality  at  a  pressure  of  100  Ibs.  absolute 
and  rejects  steam  at  a  pressure  of  15  Ibs.  absolute.     The  engine  used  30  Ibs.  of  steam 
per  horse-power  per  hour.     Find  the  efficiency.  Ans.     8.6%. 

2.  Find  the  loss  due  to  radiation  in  the  above  problem,  if  the  steam  exhausted 
is  of  91  per  cent  quality.  Ans.     20  B.T.U.  per  pound  of  cylinder  feed. 

3.  A  pressure  of  75  Ibs.  gage  raises  the  pencil  point  of  an  indicator  1£  ins.  above 
the  atmospheric  line.     What  is  the  scale  of  the  spring?  Ans.  50  Ibs. 


124  THE  STEAM   ENGINE  ART.  149 

4.  An  indicator  card  has  an  area  of  3.5  sq.ins.  and  a  length  of  3  ins.;  find  the  mean 
effective  pressure  when  the  scale  of  the  spring  is  40  Ibs. 

Ans.     46.7  Ibs.  per  square  inch. 

5.  The  area  of  the  piston  of  an  engine  is  100  sq.ins.    The  mean  effective  pressure 
is  40  Ibs.  per  square  inch.     The  length  of  stroke  is  2  ft.  and  the  engine  makes  150 
revolutions  per  minute.     The  engine  is  double  acting.     Compute  its  horse-power. 

Ans.     72.7  H.P. 


CHAPTER   IX 
STEAM   CYCLES 

150.  The  Carnot  Cycle  for  Dry  and  Saturated  Steam.  The  principal 
factor  in  the  cost  of  steam  engine  operation  is  the  efficiency  of  the  engine, 
which  may  be  denned  as  the  ratio  of  the  work  done  by  the  engine  to  the 
heat  supplied  to  the  engine.  The  efficiency  of  the  engine  depends 
primarily  upon  the  .efficiency  of  the  cycle  performed  by  the  working  fluid 
in  the  engine  cylinder.  It  is  therefore  in  order  to  investigate  the  efficiencies 
of  the  various  cycles  employed  in  actual  engines,  and  the  methods  by  which 
these  efficiencies  may  be  increased.  This  chapter  will  not  deal  with  those 
losses  which  are  due  to  the  imperfection  of  the  materials  or  mechanism 
of  the  engine,  but  only  with  those  which  are  due  to  the  cycle  performed 
by  the  working  fluid. 

In  theory  there  are.  many  different  cycles  which  may  be  .performed 
by  the  working  fluid  of  a  steam  engine.  The  most  efficient  of  these  is  the 
Carnot  cycle.  In  order  to  carry  out  the  Carnot  cycle  in  a  steam  engine  using 
dry  and  saturated  steam,  the  steam  must  be  evaporated  in  the  cylinder 
instead  of  in  a  separate  boiler,  and  condensed  in  the  cylinder,  instead  of 
being  rejected  to  the  air  or  to  a 
separate  condenser.  The  indicator 
card  of  the  Carnot  cycle  for  a  steam 
engine  is  shown  in  Fig.  56.  The 
volume  of  the  water  is  the  length  of 
the  abscissa  to  point  a.  The  volume 
of  the  steam  formed  is  the  length  of 
the  abscissa  to  point  b.  As  soon  as  FlG>  56._ Carnot  cycle  for  dry  and 

the  water  is  completely  evaporated,  saturated  steam, 

the  steam  being  dry  and  saturated, 

adiabatic  expansion  begins,  continuing  to  point  c.  During  this  adiabatic 
expansion  some  of  the  steam  condenses,  as  was  shown  in  Art.  109,  Chapter 
VI.  When  the  steam  has  expanded  to  the  temperature  of  the  cooler, 
the  back  stroke  commences,  and  the  steam  is  compressed  and  condensed 
at  constant  pressure  by  the  action  of  the  cooler,  until  point  d  of  the 
diagram  is  reached.  At  this  point  the  cooling  ceases,  and  the  mixture 
of  steam  and  water  is  then  compressed  adiabatically,  which  increases 
the  temperature  of  the  mixture,  and  since  the  mixture  is  very  wet,  con- 
denses the  remaining  steam.  At  the  end  of  this  compression  all  of  the 

125 


126 


STEAM   CYCLES 


ART.  151 


steam  has  been  condensed,  and  the  water  has  the  temperature  of  vaporiza- 
tion corresponding  to  the  pressure  at  a. 

The  efficiency  of  this  cycle  depends  solely  upon  the  absolute  temper- 
ature during  the  isothermal  expansion  and  compression  from  a  to  b 
from  c  to  d,  and  was  shown  in  Chapter  IV  to  be 

E  =  — m , 


in  which  E  is  the  efficiency  of  the  cycle,  T\  is  the  absolute  temperature 
of  the  steam  during  evaporation,  and  T2  is  the  absolute  temperature 
of  the  steam  during  condensation.  Such  a  cycle  is  obviously  imprac- 
ticable in  the  case  of  steam,  as  no  mechanism  can  be  devised  which  will 
reproduce  it  exactly.  We  may,  however,  reproduce  it  approximately 
by  methods  which  will  be  described  later.  • 


FIG.  57. — Steam  initially  superheated. 


FIG.  58. — Steam  initially  wet. 


151.  The  Carnot  Cycle  for  Wet  or  Superheated  Steam.  The  Carnot  cycle  may 
be  performed  when  using  wet  or  superheated  steam  as  a  working  fluid.  If  the  steam  is 
wet  at  point  b,  the  card  will  be  similar  in  form  to  that  shown  in  Fig.  56,  but  the  volume 
at  b  and  at  c  will  be  less  than  when  the  steam  is  dry  at  the  beginning  of  expansion. 
It  may  be  remarked  in  this  connection  1  hat  it  is  not  necessary  that  the  steam  be  entirely 
condensed  at  point  a  to  perform  a  Carnot  cycle,  provided  only  that  it  returns  to  its 
initial  state.  If  the  steam  is  highly  superheated  at  the  beginning  of  isothermal 
expansion  and  the  temperature  range  of  the  cycle  is  not  too  great,  the  steam  will  remain 
superheated  throughout  the  entire  cycle  and  the  card  given  by  the  engine  be  almost 
identical  with  that  which  would  be  given  by  a  perfect  gas.  The  form  of  the  card  is 
the  same  as  that  shown  in  Fig.  14,  Chapter  IV,  for  a  gas.  In  case  the  steam  is  not 
highly  superheated  at  the  beginning  of  isothermal  expansion  it  will  become  wet  as  a 
result  of  the  adiabatic  expansion,  the  isothermal  compression  line  will  also  be  iso- 
baric  and  the  form  of  the  card  will  be  that  shown  in  Fig.  57.  Only  a  small  portion  of 
the  steam  may  be  condensed  during  isothermal  compression,  in  this  case,  since  the 
whole  mass  of  steam  and  water  must  be  returned  to  its  original  state  by  the  adiabatic 
compression.  The  steam  may  be  initially  wet,  and  become  superheated  during  iso- 
thermal expansion,  in  which  case  the  card  will  have  the  form  shown  in  Fig.  58.  When 


ART.    152  THE   RANKINE   CYCLE  127 

superheated  steam  is  employed  as  tho  working  fluid  in  a  Carnot  engine,  the  volume  of 
cylinder  must  be  larger  for  a  given  weight  of  working  fluid  than  when  saturated  steam 
is  used.  Also  the  work  performed  by  a  given  weight  of  superheated  steam  will  be 
very  much  less  for  the  same  range  of  temperature  than  would  be  performed  by  the 
same  weight  of  saturated  steam.  The  efficiency  of  the  cycle  for  a  given  temperature 
range,  is  the  same,  whether  wet,  dry  or  superheated  steam  is  employed.  Neither 
the  Carnot  cycle  itself  nor  any  approximation  to  it  is  ever  actually  employed  hi 
connection  with  superheated  steam,  on  account  of  the  very  great  cylinder  volumes 
required  to  obtain  very  moderate  amounts  of  power. 

152.  The  Rankine  J  Cycle.  A  second  steam  cycle  is  one  which  is 
known  as  the  Rankine  cycle.  Since  this  is  the  most  efficient  cycle  which 
may  be  performed  by  steam  without  evaporating  and  condensing  the 
working  fluid  within  the  engine  cylinder,  it  has  been  adopted  as  the  standard 
of  efficiency  with  which  the  efficiency  of  all  other  cycles  may  be  compared. 
The  indicator  card  of  this  cycle  is 
shown  in  Fig.  59.  The  engine  is 
assumed  to  have  no  clearance,  and 
the  walls  of  the  cylinder  to  be  non- 
conductors of  heat.  Steam  is  admitted 
from  a  boiler  from  point  a  to  point  b, 
the  expansion  being  isothermal  (and 
isobaric)  and  the  boiler  and  steam  pipe 

being  a  part  of  the  expansion  chamber. 

FIG.  59.— Watt  diagram  of  the 

At    b    cut-off    occurs,  and  the  steam  Rankine  cycle 

contained    in    the    cylinder    expands 

adiabatically  to  the  pressure  of  the  exhaust  pipe,  as  shown  by  line  6-c, 
some  of  it  condensing  during  the  process.  At  the.  end  of  this  expansion 
the  steam  is  discharged  into  the  exhaust  pipe  at  a  constant  back  pres- 
sure, line  c-d  representing  this  process  of  isothermal  compression.  Line 
d-a  represents  the  rise  in  temperature  and  pressure  without  change  in 
volume  which  results  when  the  inlet  valve  opens. 

The  efficiency  of  the  Rankine  cycle  may  be  found  in  the  following 
manner:  During  the  period  of  admission  the  work  done  by  each  pound 
of  steam  is  equal  to  the  external  work  of  evaporation  of  steam  of  the 
temperature  of  admission  multiplied  by  the  quality  of  the  steam  admitted. 
During  the  adiabatic  expansion  the  steam  loses  intrinsic  energy,  and  the 
work  done  during  expansion  is  equal  to  the  difference  between  the  intrinsic 
energy  of  the  steam  at  the  beginning  and  at  the  end  of  the  expansion. 
The  work  done  in  forcing  the  steam  out  of  the  cylinder  against  the  back 
pressure  is  equal  to  the  external  work  of  evaporation  of  steam  at  the 
temperature  of  exhaust,  multiplied  by  the  quality  of  the  steam  exhausted. 
The  work  done  during  the  cycle  per  pound  of  steam  will  then  be  equal 

1  Often  termed  the  Clausius  Cycle. 


128  STEAM   CYCLES  ART.  152 

to  the  sum  of  the  external  work  of  evaporation  and  the  intrinsic  energy 
of  the  steam  admitted,  less  the  sum  of  the  external  work  of  evaporation 
and  the  intrinsic  energy  of  the  steam  exhausted,  which  is,  of  course, 
equal  to  the  difference  between  the  total  heat  of  the  steam  admitted  and 
the  total  heat  of  the  steam  exhausted.  If  we  know  the  pressure  (or 
temperature)  and  quality  of  the  steam  admitted,  we  may  compute  its 
total  heat  and  its  entropy.  The  entropy  of  the  steam  exhausted  is  the 
same  as  that  of  the  steam  admitted,  since  the  expansion  is  adiabatic. 
From  the  known  entropy  and  temperature  of  the  steam  exhausted,  we 
may  compute  its  quality  and  its  total  heat.  The  difference  between  the 
total  heats  is  the  work  done  per  pound  of  steam  admitted.  The  heat 
supplied  in  the  boiler  to  each  pound  of  steam  is  equal  to  the  total  heat 
of  the  steam  admitted,  less  the  heat  of  the  liquid  at  the  temperature  of 
exhaust.  We  may  therefore  express  the  efficiency  of  this  cycle  by  the 
formula 

F  =  ^JLTj^J? 
H1-h2' 

in  which  HI  is  the  total  heat  of  the  steam  admitted,  H2  is  the  total  heat 
of  the  wet  steam  discharged,  and  h2  is  the  heat  of  the  liquid  at  the  tem- 
perature of  exhaust. 

It  may  be  shown  that  the  efficiency  of  the  Rankine  cycle,  like  that 
of  the  Carnot  cycle,  is  increased  by  increasing  the  temperature  range  of 
the  working  fluid.  Referring  to  the  formula  for  the  efficiency  of  the 
Rankine  cycle  given  in  the  preceding  paragraph,  it  will  be  seen  that  an 
increase  in  the  initial  total  heat  of  the  steam  will  result  in  an  increase  of 
the  efficiency  of  the  cycle,  since  both  the  numerator  and  denominator 
of  the  fraction  will  be  increased  by  the  same  amount,  while  the  total  heat 
of  the  steam  rejected  will  be  diminished,  on  account  of  the  greater  range 
of  expansion.  Since  the  total  heat  of  the  steam  increases  with  the  pres- 
sure, it  will  be  seen  that  an  increase  in  the  initial  pressure  of  the  steam 
must  result  in  an  increase  in  the  efficiency  of  the  cycle.  An  investiga- 
tion of  the  properties  of  steam  will  show  that  when  it  expands  adiabat- 
ically,  between  any  two  temperatures,  the  decrease  in  the  total  heat  is 
greater  than  the  decrease  in  the  heat  of  the  liquid.  Consequently,  a 
downward  extension  of  the  temperature  range  of  the  Rankine  cycle  will 
add  to  the  numerator  of  the  fraction  expressing  the  efficienc}^  a  larger 
quantity  than  it  will  add  to  the  denominator,  and  the  efficiency  of  the 
cycle  will  be  increased  by  a  reduction  of  the  terminal  pressure. 

In  case  superheated  steam  is  used  in  the  Rankine  cycle,  the  form  of 
card  will  be  exactly  the  same  as  that  shown  in  Fig.  59,  except  that  the 
form  of  expansion  line  will  slightly  change  when  the  expanding  steam 
reaches  the  saturation  point.  The  efficiency  of  the  cycle  will,  of  course, 


ART.  154  THE   MODIFIED   EANKINE   CYCLE  129 

be  expressed  by  the  formula  already  given,  but  the  value  of  HI,  instead 
of  being  the  value  for  the  total  heat  of  wet  steam,  will  be  the  value  for 
the  total  heat  of  superheated  steam  of  the  given  pressure  and  temperature 
An  investigation  of  the  properties  of  superheated  steam  will  show  that 
the  greater  the  superheat  of  the  steam,  the  greater  will  be  the  efficiency 
of  the  cycle.  Since  it  is  practicable  to  use  superheated  steam  of  a  much 
higher  temperature  than  saturated  steam,  this  is  a  matter  of  importance 
in  the  theory  of  the  economy  of  the  steam  engine. 

153.  The  Modified  Rankine  Cycle.  The  Rankine  cycle  described 
in  the  preceding  paragraph  cannot  be  reproduced  in  a  steam  engine, 
since  no  engine. can  be  constructed  without  clearance,  or  of  materials 
which  are  perfect  non-conductors  of  heat.  However,  it  would  be  possible 
in  a  non-conducting  cyclinder  to  produce  a  cycle  which  is  the  thermo- 
dynamic  equivalent  of  this  cycle  by  the  method  shown  in  Fig.  60,  which 
is  the  theoretical  indicator  card  from 
an  engine  operating  on  a  modified 
Rankine  cycle.  The  engine  has  • 
the  clearance  volume  represented 
by  the  distance  from  OP  to  point 
a.  Cut-off  occurs  at  6,  adiabatic 
expansion  occurs  from  b  to  c  to 
the  pressure  of  the  exhaust,  the 
exhaust  is  discharged  at  this  pres- 


sure   from    c    to    d,    and    at    d    com-  FlG  60.— Modified  Rankine  cycle. 

pression    begins.       The    volume    at 

point  d  is  so  chosen  that  by  adiabatic  compression  of  the  entrapped 
steam,  it  will  be  raised  to  its  initial  pressure,  temperature  and  quality, 
in  passing  from  state  d  to  state  a.  An  engine  operating  on  this  cycle 
has  exactly  the  same  efficiency  as  an  engine  operating  on  the  Rankine 
cycle,  since  the  cushion  steam  does  the  same  work  during  expansion 
as  is  done  upon  it  during  compression.  However,  the  volume  of  its 
cylinder  must  be  somewhat  larger  than  that  of  an  engine  operating  on 
the  Rankine  cycle,  since  the  volume  from  c  to  d  in  each  diagram  must 
be  the  same  in  order  for  the  two  engines  to  develop  the  same  power  per 
stroke. 

154.  Computation  of  a  Rankine  Cycle.  The  following  example  will 
serve  to  make  clear  the  method  of  computing  the  efficiency  of  the  Rankine 
cycle  for  a  given  range  of  temperature  and  pressure.  Assume  that  one 
pound  of  steam  of  a  pressure  of  150  pounds  absolute  and  a  quality  of  90  per 
cent  performs  a  Rankine  cycle,  being  exhausted  at  a  pressure  of  2  pounds 
absolute.  The  total  heat  of  the  steam  will  be  h  +  qL  =  330. 2  +  90X863. 2  = 

1107.1  =  HI.      The    entropy    of    the    entering    steam   will    be    n  +  ^~  = 


130 


STEAM    CYCLES 


ART.  154 


.5142  +  . 90X1.0550=1.4637  =  ^.  The  entropy  of  the  exhaust  steam  will 
be  the  same  as  that  of  the  entering  steam  and  the  entropy  of  evapora- 
tion will  be  #2-^2  =  1.4637-0.1749=1.2888.  The  quality  of  the  steam 
exhausted  will  be 

1.2888 

1:7431= 74.0  per  cent. 

The  total  heat  of  the  steam  exhausted  will  be  94.0  +  .74 X  1021.0  =  850  =  H2. 
The  heat  of  the  liquid,  h<2  is  from  the  tables  94.0  B.T.U.  The  efficiency 
of  the  cycle  is  therefore 

1107.1-850.0 


Q 

I    . 

o  20 

>> 
§ 
.3? 


1C) 


25 


75 


100  125  150 

Initial  Absolute  Pressure 


175 


200 


225 


250 


FIG.  61. — Relation  between  the  efficiency  of  the  Rankine  cycle  and  the  initial  steam 
pressure.  Curve  I  is  for  15  Ibs.  back  pressure.  Curve  II,  is  for  2  Ibs.  back 
pressure. 

In  order  to  illustrate  the  effect  of  changing  the  temperature  or  pres- 
sure range  upon  the  efficiency  of  the  Rankine  cycle,  the  curves  shown  in 
Figs.  61  and  62  are  drawn.  The  curves  in  Fig.  61  show  the  effect  of 
varying  the  initial  pressure  for  various  constant  back  pressures,  while 
those  in  Fig.  62  show  the  effect  of  varying  the  back  pressure  for  various 
constant  initial  pressures.  It  may  be  noted  in  connection  with  the 
efficiency  of  this  cycle,  that  the  cycle  is  most  efficient  when  dry  steam  is 
used  and  that  when  wet  steam  is  used  the  efficiency  gradually  falls  off, 


ART.  155 


THE   RANKINE   JACKETED   CYCLE 


131 


as  is  shown  by  the  curve  in  Fig.  63.  The  effect  of  increasing  the  super- 
heat is  shown  in  the  same  figure.  That  part  of  the  diagram  lying  to  the 
left  of  the  heavy  vertical  line  is  the  region  of  wet  steam,  while  that  lying 
to  the  right  is  the  region  of  superheated  steam. 

155.  The  Rankine  Jacketed  Cycle.  In  order  to  minimize  the  loss 
resulting  from  cylinder  condensation,  it  is  often  found  advisable  to  heat 
the  walls  of  the 
steam  engine  cylin- 
der by  surrounding 
them  with  a  jacket 
or  steam  space,  con- 
taining steam  at 
boiler  pressure.  Wet 
steam  readily  ab- 
sorbs heat  both  by 
conduction  and  ra- 
diation, while  dry 
steam  does  not  ab- 
sorb heat  readily. 
As  the  steam  in  the 
engine  cylinder  ex- 
pands, it  tends  to 
condense  and  its 
temperature  falls. 
The  wet  steam  in 
the  cylinder  con- 
sequently tends  to 
absorb  heat  from 
the  cylinder  walls, 
which  in  turn  ab- 

,1  ,,  ,,  0        2       4       6       8       10      12      U      16      18 

sorb    heat  irom   the  Absolute  Back  Pressure, 

steam       jacket,       so        FIG.  62.— Relation  between  the  efficiency  of  the  Rankine 
that     the    steam    in  cycle  and  the  back  pressure, 

the   engine   cylinder 

is  maintained  in  practically  a  dry  condition  throughout  the  whole 
range  of  expansion,  but  is  not,  at  any  time,  appreciably  superheated. 
In  consequence  of  these  facts,  when  a  steam  cylinder  is  thoroughly 
jacketed,  the  steam  within  the  cylinder  performs  a  cycle,  usually 
termed  the  jacketed  cycle,  throughout  which  it  is  assumed  to  remain 
in  a  dry  and  saturated  condition.  The  theoretical  indicator  card 
given  by  an  engine  operating  on  the  jacketed  cycle,  with  complete 
expansion,  is  shown  in  Fig.  64.  Dry  steam  is  admitted  from  a  to  b. 
During  expansion  the  steam  remains  in  a  dry  and  saturated  condition 


132 


STEAM    CYCLES 


ART.  155 


30 


15 


10 


and  line  c-d  is  therefore,  a  line  of   constant  steam  weight.     The   heat 

necessary  to  main- 
tain the  steam  in 
this  condition  is 
supplied  from  the 
jacket  by  the  lique- 
faction of  the  steam 
contained  therein. 
At  the  end  of  expan- 
sion dry  and  satura- 
ted steam  is  rejected 
to  the  exhaust. 

The  efficiency  of 
the  Rankine  jacket- 
ed cycle  with  com- 
plete expansion  is 
less  than  that  of  the 
uiijacketed  cycle,  as 
may  be  shown  in  the 
following  manner. 
Referring;  to  Fig.  65, 
a-b-d-c  is  the  pres- 
sure volume  diagram 
of  the  Rankine  un- 
jacketed  cycle  for  1 
pound  of  steam,  and 
a-e-f-d  is  the  dia- 
gram of  the  Rankine 
uiijacketed  cycle, 


10      20      30       40      50      60       70      80      90     100  °g  §  § 

Quality  %  „  ^  &I&  , 

Superheat 

in  Degrees. 

FIG.  63. — Relation  between  the  efficiency  of   the    Rankine 
cycle  and  the  quality  of  the  steam. 


when  the  quantity  of  steam  taken  is  such  that  the  amount  of  dry  steam 
in  the  cylinder  at  the  end  of  expansion  is  1  pound,     b  e  f  c  is  then  the 


FIG.  64. — Card  for  a  Rankine  jacketed 
cycle. 


FIG.  65. — Showing  the  efficiency  of  the 
jacketed  cycle. 


ART.  156     EFFICIENCY  OF  JACKETED  CYCLE  WITH  WET  STEAM     133 

equivalent  of  a  Rankine  cycle  whose  efficiency  will  be  the  same  as  the 
efficiency  of  either  of  the  other  two  cycles.  The  line  b-f  is  the  line  of 
constant  steam  weight,  or  the  expansion  line  of  the  Rankine  jacketed 
cycle  for  1  pound  of  steam.  The  quantity  of  heat  supplied  by  the  jacket 
is  equal  to  that  represented  by  the  area  b-f-c  plus  the  heat  rejected  by 
the  Rankine  cycle  b-e-f-c.  If  we  represent  the  heat  rejected  by  R}  the 
heat  equivalent  of  the  area  b-f-c  by  J  and  of  the  area  b-e-f-c  by  U, 
we  will  have  for  the  efficiency  of  the  heat  supplied  by  the  jacket, 


J  +  R' 

wh'le  the  efficiency  of  the  heat  supplied  in  the  cylinder  feed  of  an  unjack- 
eted  cycle  will  be  represented  by  the  formula 

U_ 

=   U~+  R' 

Since  U  is  much  larger  than  J,  it  will  be  seen  that  the  efficiency  of  the 
heat  supplied  by  the  jacket  is  much  less  than  if  this  heat  had  been  supplied 
in  the  cylinder  feed.  Consequently,  the  efficiency  of  the  jacketed  cycle 
will  be  less  than  the  efficiency  of  the  unjacketed  cycle. 

The  quantity  of  work  done  during  the  jacketed  cycle  may  be  determined 
by  writing  an  empirical  equation  which  expresses  the  relation  between 
the  pressure  and  volume  of  dry  and  saturated  steam  for  the  range  of 
expansion  of  the  cycle,  and  so  obtaining  the  work  done  under  the  expan- 
sion line.  The  total  work  done  during  the  cycle  will  be  the  work  done 
under  the  expansion  line  plus  the  external  work  of  evaporation  of  steam 
at  the  initial  pressure,  less  the  external  work  of  evaporation  of  steam  at 
the  exhaust  pressure.  The  heat  rejected  per  pound  of  working  fluid  will 
be  the  latent  heat  of  evaporation  of  the  steam  at  the  exhaust  pressure. 
The  heat  supplied  will  be  the  sum  of  the  heat  rejected  and  the  work  done. 
The  heat  supplied  from  the  cylinder  feed  will  be  equal  to  the  total  heat  of 
steam  at  the  initial  pressure  less  the  heat  of  the  liquid  at  exhaust  pressure. 
The  heat  supplied  by  the  jacket  will  be  equal  to  the  total  heat  supplied 
less  the  heat  supplied  in  the  cylinder  feed.  The  number  of  pounds  of 
jacket  feed  per  pound  of  cylinder  feed  will  be  found  by  dividing  the  latent 
heat  of  evaporation  at  the  initial  pressure  by  the  heat  supplied  by  the 
jacket  per  pound  of  cylinder  feed. 

156.  Efficiency  of  the  Jacketed  Cycle  with  Wet  Steam.  In  case  the  steam  sup- 
plied to  a  jacketed  engine  is  wet,  the  efficiency  of  the  cycle  will  be  seriously  reduced, 
since  the  wet  steam  will  be  evaporated  during  the  expansion  period  and  will  not  perform 
the  work  which  it  would  otherwise  do.  A  jacketed  engine  in  theory  always  rejects 
dry  and  saturated  steam.  Practically  the  steam  contains  a  very  small  percentage 
of  moisture.  No  theory  can  be  developed  for  the  jacketed  cycle  on  the  assumption 


134  STEAM   CYCLES  ART.  157 

that  the  steam  is  initially  wet,  unless  the  form  of  expansion  line  is  also  assumed.  In 
the  case  of  an  actual  engine,  it  may  be  assumed  that  the  expansion  line  has  the  form 
PVn=K,  and  the  value  of  the  index  n  may  be  determined  from  the  indicator  card. 
The  theory  of  the  cycle  may  then  be  developed  after  finding  the  initial  and  final  quality 
of  the  steam  from  the  known  cylinder  volume  and  cylinder  feed. 

157.  The  Imperfect  Cycle  without  Clearance.  In  the  actual  steam 
engine  it  is  not  practicable  to  expand  the  steam  completely  (i.e.,  to 
expand  it  till  its  pressure  equals  the  back  pressure)  for  several  reasons. 
In  the  first  place,  it  is  necessary,  in  order  to  govern  the  speed  of  the  engine, 
to  have  a  variable  terminal  pressure  when  the  load,  or  quantity  of  power 
developed  by  the  engine,  varies.  In  the  next  place,  it  will  be  found  that 
the  friction  of  the  engine  will  be  very  greatly  increased  if  the  cylinder  is 
made  large  enough  to  allow  of  complete  expansion.  In  addition,  there 
are  certain  losses  which  are  increased  by  increasing  the  ratio  of  expansion 
of  the  steam.  In  order  to  minimize  these  losses,  the  cycle  adopted  in 
practical  work  is  of  the  form  already  described  in  Fig.  29. 

The  effect  of  introducing  terminal  drop  (i.e.,  a  difference  between  the 
terminal  and  exhaust  pressure),  is  of  course  to  reduce  the  quantity  of 
work  performed  by  a  given  weight  of  steam.  This  may  be  shown 
graphically  by  the  theoretical  card  in  Fig.  66,  which  is  the  card  of  an  engine 
expanding  steam  adiabatically  from  an  initial  pressure  of  100  pounds 

per  square  inch  to  a  final  pressure  of 
16  pounds  per  square  inch.  The  lines 
a— a,  b-b,  c-c,  and  d-d  represent  the 
drop  in  pressure  at  the  end  of  the 
stroke,  wrhen  the  ratio  of  expansion 
is  one,  two,  three,  and  four.  The 
area  included  within  the  lines  repre- 
sents the  quantity  of  work  performed 

by  the  steam.     The  quantity  of  steam 
FIG.  66. — Card   showing  the   loss   due  .      ,  .     ,, 

to  incomplete  expansion.  required  is  the  same  in  each  case,  but 

it  will  be  seen  that  the  greater  the 

ratio  of  expansion,  the  greater  the  quantity  of  work  which  this  steam  will 
perform.  The  effect  of  introducing  terminal  drop  is  therefore  to  increase 
the  thermodynamic  loss  of  the  cycle,  and  to  reduce  the  other  losses  in 
the  engine.  That  terminal  drop  is  chosen  which  makes  the  sum  of  the 
practical  losses  and  the  theoretical  loss  a  minimum. 

It  may  be  noted  that  when  the  steam  expands  to  a  pressure  lower  than 
the  exhaust  pressure,  not  only  are  the  actual  losses  still  further  increased, 
but  the  efficiency  of  the  cycle  is  reduced.  Fig.  67  is  the  indicator  card 
for  such  a  cycle.  When  the  exhaust  valve  opens  at  point  d}  air  or  steam 
will  rush  into  the  cylinder  from  the  exhaust  pipe,  increasing  the  pres- 
sure to  e.  This  air  or  steam  must  be  expelled  against  the  back  pressure. 


ART.  157    THE  IMPERFECT  CYCLE  WITHOUT  CLEARANCE 


135 


It  does  no  work  while  it  is  entering  the  cylinder,  but  in  expelling  it  from 
the  cylinder,  work  is  done  upon  it  represented  by  the  area  c—d—e.  It 
will  therefore  be  seen  that  power  was  lost  as  a  result  of  the  expansion 
below  the  back  pressure. 

The  work  done  during  a  cycle  in  which  there  is  terminal  drop,  but 
no  clearance,  may  be  found  by  treating  the  cycle  as  though  it  consisted 
of  two  parts,  a  Rankine  cycle  (area  a—b—c—f  in  Fig.  68)  whose  back  pres- 
sure is  equal  to  the  terminal  pressure,  and  a  second  cycle  (area  c—d—e-f) 
in  which  the  work  done  is  equal  to  the  product  of  the  difference  between 
the  terminal  pressure  and  exhaust  pressure  in  pounds  per  square  foot 
into  the  terminal  volume  in  cubic  feet.  The  terminal  volume  per 
pound  of  cylinder  feed  may  be  discovered  by  multiplying  the  specific 
volume  of  steam  at  the  terminal  pressure  by  the  quality  of  the  steam  at 


FIG.  67. — Loss  due  to  extreme 
expansion. 


FIG.  68. — Work  done  during  a 
Rankine  cycle. 


the  end  of  expansion.  The  quality  may  of  course  be  obtained  from  the 
known  initial  and  final  conditions.  Designating  the  total  heat  of  the 
steam  at  admission  by  HI,  at  the  terminal  pressure  by  Htj  the  terminal 
volume  in  cubic  feet  by  Vt,  the  terminal  pressure  in  pounds  per  square 
foot  by  Pt,  the  exhaust  pressure  by  P2,  and  the  heat  of  the  liquid  at  the 
temperature  of  exhaust  by  h2,  we  will  have  for  the  work  in  foot  pounds 
during  the  imperfect  cycle  without  clearance 


U  =  J(H!-Ht)  +  (Pt-'P2)Vt. 
For  the  efficiency  of  the  cycle,  we  will  have 

U 


E  = 


J(H1-h2y 


In  Fig.  69  will  be  found  curves  showing  the  relation  between  the 
terminal  pressure  and  the  efficiency  for  different  rondrtions  of  initial  and 
exhaust  pressure. 


136 


STEAM   CYCLES 


ART.  158 


158.  The  Effect  of  Clearance.     It  has  already  been  shown  that  in 
case  expansion  and  compression  are  complete,  the  efficiency  of  the  cycle 


30 


25 


15 


10 


20 


60 


140 


160 


180         300 


80  1UO          130 

Terminal  Drop 

FIG.  69. — Relation  between  the  efficiency  of    the  imperfect  cycle  and  the  terminal 
drop  in  Ibs.  per  sq.in. 

Curve  I.  For  100  Ibs.  initial  and  15  Ibs.  back  pressure. 
Curve  II.  For  100  Ibs.  initial  and  2  Ibs.  back  pressure. 
Curve  III.  For  190  Ibs.  initial  and  1  Ib.  back  pressure. 

is  not  altered  by  clearance.     Usually,  however,  the  efficiency  of  the  cycle 
is  reduced  by  clearance,  as  may  be  seen  from  the  following  considerations: 

The  two  simplest  cases  of  loss  from 
clearance  are  first,  when  the  compres- 
sion is  complete  and  the  expansion 
is  incomplete,  and  secondly,  when 
the  expansion  is  complete  and  there 
is  no  compression.  In  Fig.  70  is 
the  card  of  an  engine  having  com- 
plete compression,  but  incomplete 
expansion.  Every  portion  of  the 
steam  contained  in  the  cylinder  during 
expansion  performs  work  in  propor- 
tion to  its  mass.  Consequently,  the 
net  work  performed  by  the  steam  in 
the  clearance  space  during  expansion 
During  its  compression,  the  net  work 


FIG  70. — Showing  clearance  loss  with 
incomplete  expansion. 

is  represented  by  the  area  a-f-g-h. 


ART.  159 


THE  PRACTICAL  CYCLE 


137 


FIG.  71. — Card  showing  the  effect  of  incom- 
plete compression. 


expended  upon  it  is  represented  by  the  area  a-e-h.  Consequently,  the 
net  loss  due  to  the  clearance  is  represented  by  the  area  f-e-g.  The  loss 
occurring  in  the  second  case  may  be  understood  by  referring  to  Fig.  71,  which 
is  an  indicator  card  for  1  pound 
of  steam  expanding  to  back 
pressure.  Every  portion  of  this 
steam  performs  work  during  the 
cycle  in  proportion  to  its  mass. 
Assume  that  the  engine  has  a 
clearance  represented  by  the  ab- 
scissa to  point  6  on  the  diagram. 
The  steam  contained  in  the  clear- 
ance space  at  the  end  of  compres- 
sion, if  compressed  adiabatically, 
would  return  by  the  path  f-a  to  its  initial  condition.  The  quantity  of 
steam  introduced  during  admission  period  is  represented  by  the  volume  a-c. 
All  of  this  steam  does  work  during  expansion,  but  that  portion  of  it 
represented  by  the  volume  a— 6  does  no  work  during  admission,  except 
to  adiabatically  compress  the  steam  already  in  the  clearance  space  at 
point  /.  Consequently,  the  area  a-b-f  represents  the  work  lost  on 
account  of  clearance. 

159.  The  Practical  Cycle.  In  the  practical  cycle  expansion  is  incom- 
plete and  we  have  both  clearance  and  incomplete  compression.  It  is 
therefore  in  order  to  determine  the  effect  of  these  various  elements  on 
the  efficiency  of  the  cycle.  Referring  to  Fig.  72,  it  may  be  seen  that  if 

the  steam  contained  in  the  clearance 
space  at  point  /,  which  is  the  point 
of  compression,  were  compressed 
adiabatically  to  the  initial  pressure, 
it  would  have  the  volume  represented 
by  the  abscissa  to  point  a.  The 
quality  of  the  steam  at  /  is,  in 
theory,  the  quality  which  the  steam 
would  have  after  expanding  adiabati- 
incom-  cally  from  its  initial  to  its  terminal 
pressure,  since  the  steam  which  re- 
mains in  the  cylinder  expels  by  its 

adiabatic  expansion  the  steam  which  escapes  from  the  cylinder  at  the 
instant  of  release.  Consequently,  steam  compressed  adiabatically  from 
point  /  to  the  initial  pressure  would  have  the  initial  quality,  which, 
however,  would  not  be  the  quality  of  the  cylinder  feed.  Were  this 
steam  compressed  adiabatically,  it  would  do  the  same  work  during 
complete  expansion  as  was  expended  upon  it  during  compression. 


o 
FIG.    72. — Clearance   loss   with 

plete  expansion  and  compression. 


138  STEAM  CYCLES  ART.  ir,0 

However,  the  cushion  steam  expands  only  to  the  pomt  h,  whose 
pressure  is  the  terminal  pressure,  and  therefore  the  quantity  of  work 
expended  in  compressing  the  cushion  steam  exceeds  the  work  it  per- 
forms per  cycle  by  the  area  f-h-4.  The  cylinder  feed,  which  has  the 
volume  a-c,  if  working  in  a  cylinder  without  clearance,  would  perform 
work  represented  by  the  area  a—c—d—e—f.  However,  it  actually  performs 
work  represented  by  the  area  b—c—d—e—f—g,  and  area  a-b—g  represents 
the  loss  on  account  of  clearance.  The  sum  of  the  areas  a-b-g  and  h-J-i 
represent  the  total  loss  occurring  in  this  cycle  on  account  of  clearance. 
It  will  be  seen  that  the  area  h-J-i  increases  as  the  terminal  pressure  rises, 
and  is  proportional  to  the  quantity  of  cushion  steam.  By  increasing 
the  quantity  of  cushion  steam,  we  will  reduce  the  loss  represented  by  the 
area  a-b—g,  but  we  will  also  increase  the  loss  represented  by  the  area 
h—f-i.  In  theory,  the  best  results  with  a  given  clearance  are  obtained  when 
the  point  of  compression  is  made  such  that  the  sum  of  these  two  losses 
is  a  minimum  for  the  given  ratio  of  expansion.  This  usually  occurs  when 
the  compression  is  nearly  complete.  In  practice,  it  is  found  that  high 
compression  decreases  the  actual  efficiency  of  the  engine,  on  account 
of  its  effect  upon  other  losses. 

160.  Efficiency  of  the  Practical  Cycle.  The  determination  of  the 
theoretical  efficiency  of  the  practical  cycle,  on  the  assumption  that  the 
expansion  and  compression  of  the  steam  are  adiabatic,  is  a  matter  of 
some  complication.  The  method  of  computing  this  efficiency  may  be 
understood  by  referring  to  the  card  for  such  a  cycle  for  1  pound  of  steam, 
illustrated  in  Fig.  73.  In  this  computation  the  following  notation  will 

be  used :  F  is  the  weight  of  the  cylin- 
der feed  in  pounds,  C  is  the  weight 
of  cushion  steam  in  pounds,  Hb  is  the 
total  heat  of  the  steam  at  point  />, 
Hc  the  total  heat  of  the  steam  at 
point  c,  Vc  the  terminal  volume  in 
cubic  feet,  Pc  the  terminal  pressure 

73.-Work  done  by  an  imperfect   in    P°Unds    P6'    B.«luare    f°Ot'  P»    tlle 
cycje  exhaust  pressure  in  pounds  per  square 

foot,   P  is  the  pressure  at  point  /  in 

pounds  per  square  foot,  Pa  is  the  initial  pressure  in  pounds  per  square 
foot,  He  is  the  total  heat  of  the  exhaust  steam  per  pound,  Hf  the  total 
heat  of  the  cushion  steam  per  pound  at  point/, and  /^the  heat  of  the  liquid 
at  the  temperature  of  exhaust.  The. weight  of  the  working  fluid,  which 
is  F  +  C,  is  1  pound.  The  quality  of  the  steam  at  point  e  is  the  quality 
which  the  steam  would  have  in  expanding  adiabatically  from  the  initial 
pressure  and  quality  to  the  back  pressure.  The  weight  of  cushion  steam 
may  be  found  from  the  known  pressure,  volume,  and  quality  of  the  steam 


AIIT.  160  PROBLEMS  139 

•at  point  e.  The  total  heat  and  other  properties  of  the  steam  at  point 
c,  e  and  /  may  be  computed,  since  the  entropy  of  the  steam  is  the  same  at 
these  points  as  at  b.  The  card  may  now  be  divided  into  four  areas. 
Area  g-b-c-i  is  a  Rankine  cycle  for  1  pound  of  steam  and  the  work 
done  during  this  cycle  in  foot-pounds  is  J(Hb—Hc).  Area  i-c  —  d-j  is  a 
rectangle  and  the  work  done  is  VC(PC—  Pd).  Area  h-f-e-j  is  a  Rankine 
cycle  performed  by  the  cushion  steam,  and  the  work  done  in  foot-pounds 
is  /  C  (Hf  —  Hc) .  Area  g—a—f—h  is  a  rectangle  and  the  work  done  is 
equal  to  Va(Pb  —  Pf).  The  quantity  of  heat  supplied  during  the  cycle 
is  equal  to  Hb—  C  Hf  —  F  h2.  The  efficiency  of  the  cycle  is  found  by  divid- 
ing the  heat  equivalent  of  the  work  done  per  cycle  by  the  heat  supplied. 
In  case  it  is  desired  to  work  out  the  cycle  for  any  other  quantity  of  work- 
ing fluid  than  one  pound,  the  procedure  will  be  exactly  the  same  except 
that  the  total  heats  at  points  b  and  c  will  be  the  total  heats  of  the  actual 
weight  of  working  fluid. 

Since  all  of  the  heat  is  supplied  in  the  cylinder  feed,  the  quality  of  the 
cylinder  feed  may  be  determined  from  its  weight  and  the  quantity  of  heat 
supplied.  In  case  the  quality  of  the  cylinder  feed,  and  its  weight,  and 
the  weight  of  the  cushion  steam,  are  known,  the  total  heat  at  c  and 
consequently  the  volume  and  other  properties  of  •  the  working  fluid  at 
different  points  of  the  cycle,  maybe  determined  from  the  fact  that  Hb  = 
C  Hf-\-F  Ha  in  which  FHa  is  the  total  heat  of  the  cylinder  feed.  In  case 
the  volumes  at  6,  c,  and  e  are  known  and  the  quality  of  the  cylinder  feed 
is  known,  the  weight  of  the  cushion  steam  and  the  properties  of  the  work- 
ing fluid  at  different  points  of  the  cycle  may  be  computed  by  successive 
approximation . 

PROBLEMS 

1.  Steam  operated  on  a  Carnot  cycle  between  pressures  of  150  Ibs.  per  square  inch 
and  2  Ibs.   per  square  inch  absolute  will  give  what  efficiency?  Ans.     28.4%. 

2.  What  will  be  the  efficiency  of  steam  initially  dry  and  saturated  when  worked 
through  the  same  pressure  range  in  a  Rankine  cycle  engine?  Ans.     25.7%. 

3.  By  what  percent  must  the  total  cylinder  volume  in  Problem  2  be  increased  for 
the  engine,  to  operate  on  a  modified  Rankine  cycle  and  give  the   same  power,  if  the 
clearance  is  30  per  cent  of  the  total  volume  at  cut-off?  Ans.     43%. 

4.  Find  the  efficiency  of  a  Rankine  cycle  engine  taking  steam  at  90  per  cent  quality 
at  a  pressure  of  150  Ibs.  absolute  and  rejecting  it  at  a  pressure  of  2  Ibs.  absolute. 

Ans.     24.9%. 

5.  Find  the  efficiency  of  a  Rankine  cycle  engine  taking  steam  at  150  Ibs.  absolute 
and  200°  superheat  and  rejecting  it  at  a  pressure  of  2  Ibs.  absolute.        Ans.     33.4%. 

6.  A  jacketed  engine  without  clearance  and  with  complete  expansion  takes  dry 
and  saturated  steam  at  100  Ibs.  absolute,  and  rejects  dry  and  saturated  steam  at  16 
Ibs.  absolute.     Find  the  index  of  the  expansion  line.  Ans.     1.152. 

7.  Find  the  constant  of  the  above  curve  for  1  lb.  of  steam. 

Ans.     K=4S7  when  p  is  in  pounds  per  square  inch  and  V  in  cubic  feet. 


140  STEAM   CYCLES  ART.  160 

8.  Find  the  work  done  during  expansion  by  1  Ib.  of  steam. 

Ans.     104,200  ft.lbs. 

9.  Find  the  heat  added  during  expansion.  Ans.     108.1  B.T.U. 

10.  Find  the  work  of  the  cycle.  Ans.     110,800  ft.lbs. 

11.  Find  the  efficiency  of  the  cycle.  Ans.     12.80%. 

12.  Find  the  efficiency  of  a  Rankine  cycle  engine  working  dry  and  saturated  steam 
through  the  same  pressure  range.  Ans.     13.4%. 

13.  An  engine  without  clearance  takes  1  Ib.  of  steam  of  90  per  cent  quality  and 
100    Ibs.    pressure,  and    expands    it    adiabatically   to    25    Ibs.   pressure.      Find  the 
terminal  volume.  Ans.     14.96  cu.ft. 

14.  The  back  pressure  in  the  above  problem  is  2  Ibs.     Find  the  work  done  during 
the  cycle.  Ans.     148,060  ft.lbs. 

15.  Find  the  efficiency  of  the  cycle.  Ans.     19.0%. 

16.  If  the  clearance  space  in  the  above  engine  is  made  equal  to  50  per  cent  of  the 
swept  volume  to  the  point  of  cut-off,  and  compression  is  complete,  what  will  be  the 
swept  volume  for  1  Ib.  of  cylinder  feed?  Ans.  20.23  cu.ft. 

17.  What  will  be  the  work  done  per  pound  of  steam  supplied? 

Ans.     120,290  ft.lbs. 

18.  What  will  be  the  efficiency  of  this  cycle?  Ans.     14.4%. 

19.  An  engine  takes  steam  of  100  Ibs.  pressure.     The  steam  is  dry  and  saturated 
at  cut-off,  and  has  a  volume  of  4.429  cu.ft.     It  expands  adiabatically  to  30  Ibs.  pres- 
sure.    The  back  pressure  is  15  Ibs.  per  square  inch.     The  volume  of  the  cushion  steam 
at  the  point  of  compression  is  4  cu.ft.     The  pressure  at  the  end  of  compression  is  60 
Ibs.      What  is  the  clearance  volume?  Ans.     1.185  cu.ft. 

20.  What  is  the  volume  at  release?  Ans.     12.74  cu.ft. 

21.  What  is  the  weight  of  the  cushion  steam?  Ans.     .171  Ib. 

22.  What  is  the  work  done  during  the  cycle?  Ans.     78,720  ft.lbs. 

23.  What  is  the  weight  of  the  cylinder  feed?  Ans.     .829  Ib. 

24.  What  is  the  total  heat  of  the  cylinder  feed?  Ans.     990.3  B.T.U. 

25.  What  is  the  heat  supplied  in  the  boiler  to  each  pound  of  cylinder  feed? 

Ans.     1016  B.T.U. 

26.  What  is  the  efficiency  of  the  cycle?  Ans.     12.0%. 


CHAPTER  X 

i 

LOSSES   IN   THE   STEAM   ENGINE 

161.  Classification.     The  losses  which  occur  in  the  steam  engine  mo 
be  classified  under  nine  heads,  as  follows: 

1.  Unavoidable  thermodynamic  loss. 

2.  Losses  due  to  the  imperfection  of  the  cycle  employed. 

3.  Losses  due  to  the  imperfection  of  the  condensing  machinery  employed. 

4.  Losses  due  to  wire  drawing  and  fluid  friction. 

5.  Losses  due  to  cylinder  condensation. 

6.  Losses  due  to  valve  and  piston  leakage. 

7.  Losses  due  to  the  conduction  and  radiation  of  heat. 

8.  Losses  due  to  clearance. 

9.  Losses  due  to  mechanical  friction. 

162.  Loss  when  a  Perfect  Cycle  is  Employed.     The  first  of  these  losses 
cannot  be  reduced  by  any  method  whatever,  without  changing  the  temper- 
ature range  through  which  it  is  possible  for  the  working  fluid  to  operate. 
It  is  the  thermodynamic  loss  of  the  Carnot  cycle.     Expressed  as  a  frac- 

T 

tion  of  the  total  heat  supplied  this  loss  is  equal  to  ^,  in  which  rl\  is  equal 

to  the  absolute  temperature  of  the  steam  supplied  to  the  engine,  and 
T2  is  the  temperature  of  the  circulating  water  discharged  from  the  con- 
denser. In  the  case  of  an  engine  using  saturated  steam,  the  unavoidable 
thermodynamic  loss  is  fixed  on  the  one  hand  by  the  highest  steam  pres- 
sure which  it  is  safe  and  profitable  to  carry,  and  on  the  other  hand  by 
the  quantity  and  temperature  of  the  condensing  water  available.  In 
case  superheated  steam  is  employed,  the  upper  limit  of  temperature  may 
be  considerably  raised. 

163.  The  Practical  Limits  of  Pressure  and  Superheat.      The   upper 
limit  of  steam  pressure  is  usually  found  to  be  between  200  and  250  pounds 
per  square  inch,  the  corresponding  temperature  being  from  380  to  400° 
F.     Engines  operating  at  higher  pressures  than  this  usually  give  trouble ; 
difficulties  are  encountered  in  properly  constructing  and  maintaining  the 
boilers  and  pipe  lines,  and  the  increased  dangers  and  expense  of  opera- 
tion more  than  overbalance  the  resulting  gain  in  thermodynamic  efficiency. 
We  may  therefore  place  the  upper  limit  of  the  temperature  range  at  400° 
F.  or  860°  absolute  in  the  case  of  engines  using  saturated  steam. 

141 


142  LOSSES  IN  THE  STEAM  ENGINE  ART.  164 

When  superheated  steam  is  employed,  the  upper  limit  of  the  tem- 
perature range  may  be  raised  to  about  600°  F.  At  higher  temperature 
than  this,  lubrication  of  the  cylinders  and  valves  of  a  reciprocating  engine 
becomes  impossible,  and  on  account  of  excessive  expansion  and  weaken- 
ing of1  materials  of  construction,  difficulties  begin  to  be  encountered  in 
steam  turbine  operation.  The  upper  limit  of  temperature  with  super- 
heated steam  is  therefore  about  1060°  absolute. 

164.  Lowest  Practicable  Temperature  of  Condensation.     In  practice 
the  final  temperature  of  the  condensing  water  depends  on  the  quantity 
of   condensing   water   available,   and   on  its  initial  temperature.     It  is, 
however,  practically  impossible  to  secure  a  final  temperature  lower  than 
70°  F.,  except  in  winter,  or  when  a  large  supply  of  cool  condensing  water 
is  available.     In  summer,  and  especially  in  the  tropics,  the  final  temper- 
ature of  the  condensing  water  will  rise  to  100  or  110°  F.     The  lower  limit 
of  temperature  range  is  therefore  about  530  to  570°  absolute. 

165.  The  Per  Cent  of  Unavoidable   Loss.     Since   the   extreme   tem- 
perature range  practicable  for  steam  engines  is  from  1060°  absolute  to 
530°  absolute,  the  unavoidable  thermodynamic  loss  can  never  be  less 
than  50  per  cent.     Except  under  the   most  favorable   conditions  it  is, 
extremely  difficult  to  realize  a  temperature  range  greater  than  from  960° 
to  560°  absolute,  under  which  conditions  41.6  per  cent  of  the  heat  sup- 
plied is  available  for  transformation  into  work  and  58.4  per  cent  is  unavoid- 
ably lost.     In  case  saturated  steam   is  used,  the    extreme   range    will 
rarely  be  greater  than  from  860  to  560°  absolute,  in  which  case  35  per 
cent  of  the  heat  is  available,  and  65  per  cent  is  unavoidably  lost.     When 
the  engine  is  run  non-condensing  with  a  steam  pressure  of  100  pounds 
absolute,  only  about  14.7  per  cent  of  the  heat  supplied  is  available,  and 
the  unavoidable  thermodynamic  loss  is  85.3  per  cent.     Compound  con- 
densing engines  are  usually  operated  under  such  conditions  that  only 
about  15  to  25  per  cent  of  the  heat  supplied  is  available.     It  will  thus 
be  seen  that  of  the  heat  supplied  to  a  steam  engine,  from  50  to  85  per 
cent  is  unavoidably  lost,  even  when  the  engine  is  ideally  perfect  in  every 
detail. 

166.  Loss  Due   to  Imperfection   of  Cycle.     The  efficiencies   of  the 
cycles   commonly  employed  in   steam  engine  work  have   already  been 
discussed  at  length  in  Chapter  IX.     The  loss  due  to  the  imperfection 
of  the  cycle  employed,  expressed  as  a  per  cent  of  the  total  heat  supplied, 
is  equal  to  the  difference  between  the  efficiency  of  the  perfect  cycle  and 
that  of  the  imperfect  cycle  actually  employed.     It  is  better,  however, 
to  express  this  loss  as  a  per  cent  of  the  available  heat.     We  may  do  so 
by  dividing  the  difference  between  the  efficiency  of  the  perfect  cycle  and 
the  imperfect   cycle,  by  the  efficiency  of  the  perfect   cycle.     This  loss 
is  minimized  by  adopting  the  most  efficient  cycle  possible. 


ART.  168         EFFECT  OF  IMPERFECT  CONDENSER  ACTION  143 

167.  Effect  of  Imperfect  Condenser  Action.     The  effect  of  the  third 
source  of  loss  is  to  raise  the  temperature  and  pressure  of  the  steam  enter- 
ing the  condenser.     If  it  were  possible  to  bring  the  condensing  water 
and  the  steam  together  in  such  a  way  that  they  would  attain  a  common 
temperature,  and  at  the  same  time  not  introduce  air  into  the  condenser, 
the  action  of  the  condenser  would  be  perfect.     However,  in  order  to 
condense  the  steam,  it  is  necessary  that  the  final  temperature  of  the 
circulating  water"  be  somewhat  less  than  that  of  the  condensing  steam. 
The  required  temperature  difference  is  variable,  amounting  sometimes 
to  over  20°.     In  addition,  air  is  present  in  the  condenser,  and  its  presence 
prevents  the  pressure  of  the  steam  in  the  exhaust  pipe  from  reaching  the 
pressure,  and  therefore  the  temperature,  of  the  steam  in  the  condenser 
itself.     On  account  of  the  presence  of  air  and  the  imperfect  cooling  of 
the  steam,  the  temperature  range  of  the  working  fluid,  and  therefore 
the  efficiency  of  the  engine,  is  reduced.     The  loss  from  this  source  depends 
upon  the  efficiency  of  the  cycle  employed,  becoming  greater  as  the  efficiency 
of  the  cycle  increases,  hence  the  importance  of  good  condensing  machinery 
in  connection  with  steam  engines  and  turbines  of  high  efficiency.     The 
amount  of  this  loss  may  be  determined  by  computing  the  theoretical 
efficiency  of  the  cycle  employed,  at    the   observed  back  pressure   (call 
this  efficiency  E0),  and  at  the  back  pressure  corresponding  to  the  tem- 
perature  of  the   discharged   circulating   water    (call  this   efficiency   Et)} 
and  taking  their  difference   (which  is  Et  —  E0).     The  result  will  be  the 
amount  of  this  loss  expressed  as  a  per  cent  of  the  heat  supplied.     It  would 
be  more  proper,  however,  to  express  it  as  a  per  cent  of  the  total  heat  trans- 
formable into  work  by  the  cycle  employed,  which  may  be  done  by  divid- 
ing the  difference  found  above  by  the  quantity  Et. 

168.  Loss  from   Wire   Drawing   and   Steam   Friction.      The    fourth 
source  of  loss  in  the  steam  engine  arises  from  the  fact  that  a  difference 
of  pressure  is  necessary  in  order  to  force  the  steam  through  the  port 
openings  and  steam    passages  of  the  engine  at  the  necessary  velocity. 
The  loss  in  pressure  incurred  in  forcing  steam  through  a  restricted  port 
opening  at  high  velocity  is  said  to  be  due  to  wire  drawing.     The  loss  in 
pressure  incurred  on  account  of  the  roughness  and  crookedness  of  the 
steam  passages  is  said  to  be  due  to  fluid  friction.      In  each  case  the  loss 
in  pressure  is  approximately  proportional  to  the  square  of  the  velocity 
of  the  steam.     When  these  openings  and  passages  are  of  ample  area, 
so  that  the  maximum  velocity  of  the  steam  does  not  exceed  6000  to  8000 
feet  per  minute,  the  loss  of  pressure  is  very  small.      When,  however, 
the  passages  are  restricted,  and  the  valves  do  not  open  and  close  promptly, 
the  pressure  difference   becomes   considerable  and  the  area  of   the   card 
actually  given  by  the  engine  is  materially  less  than  that  of  the  theoretical 
card  which  would  be  given  by  the  engine  in  case  its  ports  were  ample, 


144  LOSSES   IN   THE   STEAM   ENGINE  ART.  169 

and  its  valves  opened  and  closed  instantly.  The  ratio  of  the  area  of 
the  actual  card  to  the  area  of  the  theoretical  card  is  termed  the  card 
factor  of  the  engine,  and  is  usually  expressed  as  a  per  cent.  The  loss  due 
to  fluid  friction  and  wire  drawing,  expressed  as  a  per  cent  of  the  work 
represented  by  the  area  of  the  theoretical  card,  is  found  by  subtracting 
the  card  factor  from  100  per  cent. 

169.  Values  of  the  Card  Factor.     The  card  factor  for  locomotives 
is  usually  from  75  to  85  per  cent.     For  ordinary  high  speed  engines  with 
ample  ports  the  card  factor  will  range  from  85  to  95  per  cent.     The   card 
factor  for  a  good  Corliss  engine  is  about  95  to  98  per  cent,  while  for  slow- 
moving  pumping  engines  equipped   with  Corliss  valves  the  card  factor 
is  practically  100  per  cent.     It  will  be  seen  that  this  loss  varies  from 
about  25  per  cent  to  less  than  1  per  cent.     It  may  be  reduced  by  making 
the  steam  and  exhaust  ports  short  and  direct,  and  of  ample  area,  and  so 
operating  the  valves  that  they  open  and  close  promptly. 

170.  The  Design  of   Engine  Ports.     The  ports  of  steam  engines  are 
usually  designed  by  making  the  cross-sectional  area  of  the  inlet  passages 
such  that  the  nominal  velocity  of  the  steam  through  them  is  from  5000 
to  9000  feet  per  minute,  and  the  area  of  the  exhaust  passages  such  that 
the  nominal  velocity  of  the  steam  through  them  is  from  4000  to  7000  feet 
per  minute.     The  nominal  velocity  of  the  steam  is  found  by  dividing 
the  piston  area  by  the  port  area  and  multiplying  the  quotient  by  the 
mean  piston  speed.     Consequently,  the  formula  for  the  design  of  ports 
will  be 

S_A 
V  ' 

in  which  P  is  the  port  area ; 
A  is  the  piston  area ; 
S  is  the  mean  piston  speed ; 
V  is  the  nominal  steam  velocity. 

Since  the  actual  piston  speed  is  variable,  and  since  some  of  the  steam 
supplied  condenses  in  the  cylinder  during  admission,  the  actual  velocit}' 
of  the  steam  in  the  inlet  and  exhaust  passages  is  from  50  to  75  per  cent 
higher  than  the  nominal  velocity,  during  some  parts  of  the  stroke.  Most 
types  of  valves  open  and  close  gradually  and  therefore  greatly  restrict 
the  port  openings  during  a  considerable  portion  of  the  stroke.  The 
effect  of  this  restriction  is  to  very  greatly  increase  the  loss  due  to  wire 
drawing.  It  is  impossible  to  estimate  the  loss  from  this  source,  except 
by  making  comparisons  with  engines  in  which  this  loss  has  been 
measured. 

171.  Cylinder   Condensation.     The    most    important    source    of    loss 
in  the  steam  engine  is  due  to  the  condensation  of  steam  upon  the  cylinder 


ART.  171  CYLINDER  CONDENSATION  145 

wall  during  the  admission  period,  and  its  subsequent  evaporation  during 
the  period  of  expansion  and  exhaust.  The  cause  of  this  loss  will  oecome 
apparent  when  we  consider  the  phenomena  which  occurred  in  the  cylin- 
der while  the  engine  is  in  operation.  The  wall  which  encloses  the  work- 
ing fluid  is  of  cast  iron  or  steel,  and  is  therefore  a  good  conductor  of  heat. 
It  has  been  shown  both  from  theory  and  by  actual  measurement  that 
the  surface  of  this  wall,  at  the  instant  of  admission,  is  somewhat  cooler 
than  the  entering  steam.  On  account  of  this  difference  in  temperature, 
at  the  instant  of  admission  some  of  the  steam  immediately  condenses 
upon  the  wall  surface,1  raising  its  temperature.  Since  the  wall  is  a  good 
conductor,  heat  begins  to  flow  from  the  surface  into  the  wall.  Were  it 
not  for  this  flow  of  heat  the  temperature  of  the  surface  would  be  instantly 
raised  to  that  of  the  entering  steam,  and  condensation  would  cease  as 
soon  as  it  began.  On  account  of  this  flow  of  heat,  the  temperature  of 
the  surface  cannot  be  raised  instantly  to  that  of  the  steam  in  contact 
with  it,  and  the  condensation  goes  on  at  a  gradually  decreasing  rate 
throughout  the  period  of  admission. 

When  expansion  begins,  the  temperature  of  the  steam  begins  to  fall, 
and  finally  it  becomes  equal  to  the  temperature  of  the  wall  surface.  At 
this  instant  condensation  ceases.  After  this  point  is  passed,  the  tem- 
perature of  the  wall  surface  is  greater  than  that  of  the  expanding  steam, 
and  the  moisture  which  has  condensed  upon  it  begins  to  evaporate,  the 
heat  now  flowing  to  the  surface  from  the  interior  of  the  wall.  As  the 
steam  pressure  continues  to  fall,  the  evaporation  becomes  so  rapid  as 
to  be  almost  explosive  in  character.  In  consequence  of  this  the  steam 
evaporated  from  the  wall  during  the  latter  part  of  the  expansion  period 
is  quite  wet.  If  the  steam  is  not  all  evaporated  by  the  end  of  the  expan- 
sion period,  and  probably  it  usually  is  not,  the  remainder  of  the  water 
is  blown  off  in  the  form  of  spray  at  the  instant  that  the  exhaust  valve 
opens  and  terminal  drop  occurs. 

During  the  exhaust  stroke  the  wall  surface  is  much  hotter  than  the 
steam  contained  in  the  cylinder,  and  therefore  the  steam  is  dried  by  the 
heat  radiated  to  it  from  the  wall.  At  the  beginning  of  compression 
the  layer  of  steam  in  immediate  contact  with  the  wall  is  superheated. 
However,  since  superheated  steam  absorbs  heat  with  difficulty,  the 
radiant  heat  from  the  wall  is  unable  to  superheat  the  main  body  of  cushion 
steam  to  any  appreciable  extent,  and  this  steam  is,  at  the  beginning  of 
compression,  practically  dry  and  saturated. 

1  It  is  on  this  account  that  it  is  necessary  to  open  the  inlet  valve  before  the  engine 
begins  its  working  stroke.  If  the  valve  is  not  so  opened,  the  pressure  in  the  cylinder 
will  not  begin  to  rise  until  the  piston  has  completed  a  portion  of  the  working  stroke, 
and  there  will  be  a  considerable  loss  in  power  without  any  change  in  the  steam  con- 
sumption of  the  engine. 


146  LOSSES  IN   THE   STEAM   ENGINE  ART.  172 

After  the  closing  of  the  exhaust  valve,  as  a  result  of  adiabatic  com- 
pression the  whole  of  the  cushion  steam  is  superheated,  and  its  temperature 
raised  above  the  temperature  of  the  cylinder  walls.  As  soon  as  its  pressure 

becomes  that  corresponding  to  the 
temperature  of  the  walls,  this  super- 
heated steam  begins  to  condense, 
exactly  as  moisture  from  the  air  con- 
denses upon  the  surface  of  a  cold 
object  whose  temperature  is  below 
the  dew-point.  In  a  great  many 
engines,  compression  is  not  carried 
to  this  point,  but  in  high  speed 
engines  with  light  load,  the  com- 

pression  is  often  sufficient  to  show 
FIG.  74.  —  Card  showing  cylinder  conden-  F 

sation  during  compression.  thls     phenomenon     by     a     sudden 

change  in  the  direction  of  the  com- 

pression line  on  the  indicator  card.  This  effect  may  be  noted  at 
a  in  Fig.  74,  where  there  is  a  decrease  in  the  volume  of  the  cushion 
steam  without  a  corresponding  change  in  pressure. 

172.  The  Amount  of  Heat  Interchanged.  Since  the  steam  alternately 
imparts  heat  to,  and  extracts  it  from,  the  cylinder  wall,  the  temperature 
of  the  wall  surface,  and  consequently  of  every  point  within  the  wall, 
undergoes  periodic  variation.  This  temperature  variation  is  a  maximum 
at  the  wall  surface,  and  grows  rapidly  less  as  the  distance  from  the  parti- 
cle to  the  wall  surface  is  increased.  The  amount  of  the  temperature 
variation  is  shown  by  Professor  Cotterill  1  to  be  given  by  the  equation 


(1) 


in  which  R  is  the  temperature  range  of  any  particle,  Rs  is  the  temperature 
range  at  the  wall  surface,  x  is  the  distance  of  the  particle  from  the  surface, 
and  m  is  determined  by  the  thermal  properties  of  the  material  of  the  wall 
and  the  periodicity  of  the  cycle.  Its  value  is  given  by  the  equation 


Nws 
m- 


In  which  N  is  the  number  of  cycles  per  second,  w  is  the  density  of  the 
metal  in  pounds  per  cubic  foot,  s  is  the  specific  heat  of  the  metal,  and  / 
is  the  specific  conductivity  of  the  metal  in  B.T.U.  per  second  per  cubic 
foot,  per  degree  difference  in  temperature. 

As  a  result  of  the  periodic  variation  in  temperature  of  the  wall  sur- 
face, a  definite  quantity  of  heat  is  imparted  to  each  square  foot  of  the 

1  See  Chapter  X  of  Cotterill's  work,  "  The  Steam  Engine." 


ART.  174  PRACTICAL  ASPECTS  OP  CYLINDER  CONDENSATION          147 

wall  by  the  steam,  and  again  rejected  by  the  wall  to  the  steam,  during 
each  revolution  of  the  engine.  This  quantity  of  heat  may  be  shown  to  be 



Q  =  KR,^^±, (3) 

in  which  Q  is  the  number  of  B.T.U.  surrendered  by  the  steam  to  each 
square  foot  of  the  wall  surface  per  cycle,  K  is  a  constant  depending  upon 
the  form  of  the  temperature  cycle  of  the  wall  surface,  Rs  is  the  temperature 
range  of  the  wall  surface,  and  w  s  f  and  N  are  as  in  the  preceding  para- 
graph. The  value  of  the  constant  K  is  unity  in  case  the  temperature 
cycle  of  the  wall  surface  is  harmonic,  and  is  very  nearly  unity  for  other 
probable  forms  of  the  cycle. 

173.  The    Practical    Aspects    of    Cylinder   Condensation.     It   might 
be  thought  that  the  loss  due  to  cylinder  condensation  could  be  deduced 
directly  from  equation  (3)  in  the  preceding  article.     This  would  be  true 
if  the  temperature  range   of  the  wall  surface   were   known.     However, 
the  temperature  range  depends  on  the  form  of  the  indicator  card,  the 
pressure  range  of  the  steam,  the  quality  of  the  steam  entering  the  cylinder 
and  the  rotational  speed  of  the  engine,  and  it  is  obviously  impossible 
to  determine  it  with  any  accuracy.     Hence  we  can  make  only  a  rough 
estimate  of  the  probable 'amount  of  cylinder  condensation  in  the  case  of 
any   particular   engine,    operating    under    given    conditions.     We    may, 
however,  readily  determine  what  changes  are  necessary  in  the  operating 
conditions  in  order  to  minimize  the  cylinder  condensation.     An  inspec- 
tion of  the  equation  will  make  it  apparent  that  the  loss  may  be  reduced: 
first,  by  reducing    the  temperature    range  of   the  wall    surface;    second, 
by  increasing  the  rotational  speed  of  the  engine;  third,  by  reducing  the 
area  of  the  wall  surface  enclosing  the  clearance  space;  and  fourth,  by 
making  the  wall  of  non-conducting  material. 

174.  Methods  of  Reducing  the  Temperature  Range  of  the  Wall  Surface. 
Five  methods  are  available  for  reducing  the  temperature    range   of   the 
wall  surface :  first,  by  increasing  the  rotational  speed  of  the  engine  ;  second, 
by  supplying  the  engine  with  dry  or  superheated  steam;  third,  by  decreas- 
ing the  ratio  of  expansion ;    fourth,  by  reducing  the  temperature  range 
of  the  steam  in  the  cylinder ;  and  fifth,  by  jacketing  the  cylinder  with  steam 
of  boiler  pressure.     The  effect  of  increasing  the  rotational  speed  of  the 
engine  is  to  increase  the  rate  at  which  the  pressure  falls  during  expansion, 
to  increase  the  rapidity  of  evaporation,  and  consequently  the  wetness 
of  the  steam  evaporated  during  the  expansion  period,  to  reduce  the  heat 
loss  from  the  wall  due  to  this  re-evaporation,  and  therefore  to  reduce  the 
temperature  range  of  the  wall  surface. 

The  effect  of  supplying  an  engine  with  wet  steam  is  to  increase  the 
quantity  of  water  deposited  upon  the  wall  surface  by  a  given  heat  transfer, 


148  LOSSES  IN  THE  STEAM  ENGINE  ART.  175 

to  increase  the  loss  of  heat  due  to  the  subsequent  re -evaporation  of  this 
water,  and  therefore  to  increase  the  temperature  range  of  the  wall  surface . 
By  -supplying  the  engine  with  dry  or  superheated  steam,  the  heat  loss 
from  the  wall  caused  by  the  re -evaporation  of  the  deposited  moisture  is 
greatly  diminished,  and  the  temperature  range  of  the  wall  surface  cor- 
respondingly reduced.  The  greater  the  superheat  of  the  steam  supplied 
the  less  the  loss  from  re-evaporation,  and  therefore  the  less  the  temperature 
range  of  the  wall  surface. 

Decreasing  the  ratio  of  expansion  reduces  the  heat  loss  during  the 
expansion  period  by  shortening  this  portion  of  the  cycle.  It  also  reduces 
the  heat  loss  by  increasing  the  terminal  drop  and  so  removing  the  moisture 
more  completely  at  the  instant  of  release,  by  its  explosive  evaporation. 

Other  things  being  equal,  it  is  apparent  that  the  temperature  range 
of  the  wall  surface  must  be  proportional  to  the  temperature  range  of  the 
steam  in  the  cylinder.  We  may  reduce  the  temperature  range  of  the 
steam  in  the  cylinder  and  also  the  ratio  of  expansion,  by  using  a  multiple 
expansion  engine.  In  the  case  of  a  compound  engine,  the  temperature 
range  of  the  steam  is  reduced  to  one-half,  and  in  the  case  of  a  triple  expan- 
sion engine  to  one-third  of  its  value  for  a  simple  engine  of  the  same  pres- 
sure range.  The  cylinder  condensation  is  reduced  by  a  still  larger  amount, 
since  the  ratio  of  expansion  is  also  reduced. 

The  effect  of  a  steam  jacket  is  .to  raise  the  mean  temperature  of  the 
cylinder  wall  and  therefore  to  reduce  the  initial  condensation.  Since 
less  steam  is  condensed,  less  heat  will  be  lost  by  its  re-evaporation,  and  the 
effect  of  the  jacket  is  therefore  to  greatly  reduce  the  temperature  range 
of  the  wall  surface.  A  steam  jacket  properly  applied  always  increases 
the  efficiency  of  an  engine,  since  the  thermodynamic  loss  due  to  the  use 
of  the  jacket  is  always  less  than  the  reduction  effected  by  the  jacket  in  the 
loss  from  cylinder  condensation.  However,  the  effect  of  the  jacket  in 
increasing  the  economy  of  large  engines  of  high  piston  speed  is  insignifi- 
cant, and  the  cost  of  applying  the  jacket  to  such  engines  does  not  war- 
rant the  slight  saving  resulting  from  its  use.  Jackets  are  therefore  not 
usually  applied  to  engines  having  a  rotational  speed  of  more  than  GO  to 
75  revolutions  per  minute,  unless  they  are  desirable  for  operating  reasons, 
as,  for  instance,  to  enable  the  engineer  to  quickly  warm  up  the  engine 
when  starting. 

175.  Effect  of  Increasing  the  Speed  of  Rotation.  It  has  already  been 
shown  that  increasing  the  rotational  speed  of  the  engine  affects  the  amount 
of  cylinder  condensation  indirectly  by  reducing  the  temperature  range  of 
the  wall  surface.  An  inspection  of  Equation  (3)  Art.  172,  will  show  also 
that  it  affects  this  loss  directly,  the  amount  of  the  loss  for  a  given  tem- 
perature range  being  inversely  proportional  to  the  square  root  of  the 
number  of  revolutions  per  minute.  On  both  of  these  accounts  it  is 


AET.  178  REDUCING  THE   CLEARANCE  AREA  149 

desirable  that  an  engine  should  be  operated  at  a  high  rotational  speed. 
The  general  design  of  high  speed  engines,  however,  is  usually  such  as  to 
make  them  very  wasteful  of  steam  on  account  of  the  type  of  valve 
employed,  the  large  clearance  volume,  the  heavy  compression,  and  the 
great  area  of  clearance  surface.  In  practice  the  greatest  steam  economy 
is  obtained  from  an  engine  of  long  stroke  and  high  piston  speed,  but  of 
comparatively  low  rotational  speed. 

176.  Reducing  the  Clearance  Area.     The  area   of    the   wall  surface 
upon  which  cylinder  condensation  occurs  may  be  reduced  by  making 
the  steam  and  exhaust  ports  short  and  direct  and  by  giving  the  engine 
a   high  piston  speed.      The    high  speed   automatic   engine   usually  has 
long  and  crooked  ports,  and  being  of  very  short  stroke  has  a  low  mean 
piston   speed.     Consequently,   the    loss    from    cylinder   condensation    is 
greater  in  such  engines  than  it  is  in  long-stroke  four-valve  engines  of  equal 
power,  which  have  short,  direct  ports  and  high  piston  speed. 

It  must  be  borne  in  mind  that  it  is  not  the  cylinder  condensation 
per  cycle  which  the  designer  should  seek  to  minimize,  but  rather  the 
cylinder  condensation  per  pound  of  steam  supplied.  Increasing  the  rota- 
tional speed  of  an  engine  by  shortening  the  stroke,  and  without  changing 
the  piston  speed,  will  reduce  the  weight  of  cylinder  feed  per  revolution 
in  greater  ratio  than  it  reduces  the  weight  of  cylinder  condensation  per 
revolution,  and  will  therefore  increase  the  loss  from  condensation.  For 
mechanical  reasons  it  is  advisable  to  limit  the  mean  piston  speed  to  1000, 
or  at  the  utmost  1200  feet  per  minute,  while  speeds  of  600  to  900  feet  are 
usually  employed.  The  length  of  stroke  is  determined  by  financial 
considerations,  long-stroke  engines  being  more  expensive  for  a  given 
power  than  short -stroke  engines.  In  practice  the  stroke  is  usually 
limited  to  three  times  the  diameter  of  the  high  pressure  cylinder,  and  is 
rarely  greater  than  6  feet. 

177.  The  Use  of   a   Non-Conducting   Wall.     The  application  of  non- 
conducting materials  to  those  parts  of  the  clearance  surface  that  are  not 
subject  to  wear  has  often  been  advocated.     However,  actual  tests   of 
engines  in  which  the  clearance  surfaces  have  been  covered  with  porcelain, 
glass,  slate  or  other  non-conducting  materials,  have  not  usually  shown 
sufficient  gain  in  economy  to  warrant  the  use  of  this  method  of  reduc- 
ing cylinder  condensation.     In  general,  such  tests  have  shown  but  little 
increase  in  economy,   although   Thurston   has   reported   a   reduction  of 
60  per  cent  in  the  amount  of  cylinder  condensation  from  the  use  of  this 
method.     It  is  highly  probable,  however,  that  the  steam  jacket  is  a  more 
efficient  and  practical  method  of  reducing  the  loss. 

178.  Weight  of  Steam  Condensed  Per  Revolution.     It  is  apparent 
from  the  foregoing  discussion  of  cylinder  condensation  that  it  is  impossible 
to  derive  a  rational  formula  which  will  give  accurately  the  amount  of 


150  LOSSES  IN  THE  STEAM  ENGINE  ART.  I7fi 

steam  condensed  per  revolution  when  the  dimensions  of  the  engine, 
the  conditions  of  operation,  and  the  form  of  indicator  card  are  known. 
However,  a  large  number  of  empirical  equations  have  been  developed 
by  which  this  quantity  may  be  determined  with  more  or  less  accuracy. 
An  investigation  of  a  large  number  of  engine  tests  serves  to  show  that  the 
amount  of  cylinder  condensation  may  be  determined  approximately 
by  the  equation 


in  which  C  is  the  number  of  pounds  of  steam  condensed  per  revolution, 

A  is  the  number  of  square  feet  of  wall  surface  exposed  per  revolu- 
tion to  the  action  of  the  steam  at  cut-off, 

Rx  is  the  temperature  range  of  the  steam  during  the  expansion 
period  in  degrees  Fahrenheit, 

R  is  the  total  temperature  range  of  the  steam,  and 

•N  is  the  number  of  revolutions  per  minute. 

The  application  of  this  formula  will  be  readily  understood  from  the 
following  example:  An  engine  having  a  12"X36"  high  pressure  cylinder 
takes  steam  at  160  pounds  absolute.  The  ratio  of  expansion  is  3  and 
the  back  pressure  is  30  pounds  absolute.  The  area  of  wall  surface  exposed 
to  the  action  of  steam  at  cut-off  is  16  square  feet.  The  number  of 
revolutions  per  minute  is  125.  Required  the  weight  of  steam  condensed 
per  revolution. 

[  Assuming  hyperbolic  expansion,  the  pressure  at  release  will  be  one- 
third  the  initial  absolute  pressure,  or  53  pounds  per  square  inch.  The 
temperature  of  the  steam  at  admission  is  364°,  at  release  285°  and  at  the 
back  pressure  250°.  The  temperature  range  during  expansion  is  79° 
and  the  entire  temperature  range  is  114°.  Substituting  in  the  formula 
we  will  have 

779  4- 1 14  \ 
C=  .00033 X 16 (123.688  )  =  -069  lbs- 

The  weight  of  steam  condensed  per  stroke  is  therefore  about  .035  pound. 
By  adding  this  quantity  to  the  cylinder  feed  per  stroke  shown  by  the  card, 
the  probable  weight  of  steam  consumed  per  stroke  of  the  engine  may  be 
computed. 

In  computing  the  area  of  the  wall  surface  exposed  to  the  action  of 
the  steam  per  revolution  at  cut-off,  it  is  necessary  to  divide  this  surface 
into  three  parts.  The  first  part  is  the  area  of  the  cylinder  head  and  the 
piston.  The  second  part  is  the  area  of  the  walls  enclosing  the  ports  and 
steam  passages,  together  with  the  valve  faces.  The  third  part  is  the 
surface  of  the  cylinder  ban-el  up  to  the  point  of  cut-off.  The  first  and 
third  parts  may  be  computed  from  the  generp]  dimensions  of  the  engine, 


ART.  ISO  VALVE  AND  PISTON  LEAKAGE  151 

while  the  second  part  must  be  computed  from  the  detail  drawings  of  the 
engine  cylinder.  The  areas  must  be  computed  for  both  the  head  and 
crank  end  of  the  cylinder  and  their  sum  taken,  when  the  steam  condensed 
per  revolution  is  desired. 

179.  Valve  and  Piston  Leakage.     The  importance  of  the  sixth  source 
of  loss  in  the  steam  engine  will  depend  upon  the  design,  the  workmanship 
and  the  method  of  operation  of  the  engine.     The  leakage  past  the  piston 
of  .a  steam  engine  ought  to  be  very  slight,  in  practice,  if  the  piston  is 
properly  made  and  provided  with  properly  fitted  packing  rings.     It  is 
usual  to  make  the   piston  from  .005  to  .015  inch  smaller  in   diameter 
than  the  cylinder,  and  then  to  provide  the  piston  with  two  elastic  packing 
rings  which  expand  and  prevent  the  escape  of  steam.     In  case  these 
rings  are  broken,  or  lose  their  elasticity,  the  loss  from  piston  leakage  may 
become  a  considerable  quantity,  but  this  rarely  happens  when  the  engine 
receives  proper  care. 

A  valve  which  is  forced  down  upon  its  seat  by  an  unbalanced  steam 
pressure  will  be  steam  tight  after  it  has  worn  to  a  good  bearing.  When 
such  a  valve  is  new,  however,  although  the  surfaces  of  the  valve  and  seat 
may  be  scraped  to  an  exact  plane  while  cold,  the  valve  will  not  necessarily 
be  tight  when  it  is  hot.  The  heat  and  the  pressure  of  the  steam  upon 
the  back  of  the  valve  invariably  tend  to  distort  these  surfaces.  The 
high  spots  soon  wear  down,  however,  and  the  valve  becomes  tight.  A 
Corliss  valve,  like  a  slide  valve,  tends  to  wear  tight.  It  will  be  seen, 
therefore,  that  a  plain  slide  valve,  a  Corliss  valve,  and  a  properly  fitted 
poppet  valve,  will  not  leak  under  service  conditions. 

Piston  valves  and  balanced  slide  valves,  on  the  other  hand,  are  prac- 
tically certain  to  leak.  In  order  that  the  valve  shall  slide  freely,  it  is 
necessary  that  the  distance  between  the  balance  plate  and  the  valve 
seat  shall  exceed  the  thickness  of  the  valve  by  from  0.003  inch  to 
0.005  inch.  In  the  case  of  a  piston  valve,  a  similar  difference  is  required 
between  the  diameter  of  the  valve  and  the  valve  seat.  In  consequence 
of  this  fact,  when  such  a  balanced  valve  is  reciprocated,  there  is  a  very 
considerable  space  through'  which  steam  and  water  may  find  their  way 
directly  from  the  steam  chest  to  the  exhaust  port.  No  definite  value 
can  be  set  for  the  amount  of  this  loss,  since  it  will  depend  on  the  clearance 
of  the  valve,  on  the  value  of  the  steam  and  exhaust  pressure,  on  the  lap 
of  the  valve,  and  on  the  kind  and  amount  of  lubricant  used  on  the  valve. 
The  amount  of  this  leakage  per  revolution  is  often  equal  to  or  greater 
than  the  amount  of  cylinder  condensation  per  revolution. 

180.  Effects   of  Leakage  upon   the  Indicator  Card.      The  effect   of 
valve  and  piston  leakage  upon  the  indicator  card  of  a  steam  engine  is 
exactly  the   same   as  that  of  cylinder  condensation.     A  leak  past  the 
piston,  or  from  the  cylinder  into  the  exhaust,  during  the  admission  period, 


152  LOSSES  IN  THE  STEAM   ENGINE  ART.  181 

gives  exactly  the  same  effect  as  does  initial  condensation.  A  leak  from 
the  steam  chest  into  the  cylinder  during  the  expansion  period  gives  the 
same  effect  as  re-evaporation.  There  is  no  way  by  which  the  effects  of 
cylinder  condensation  and  re-evaporation  may  be  separated  from  those 
of  leakage  in  the  case  of  an  engine  test,  or  by  which  the  amount  of  either 
may  be  determined,  and  they  must  therefore  be  considered  together 
in  *an  analysis  of  such  a  test.  However,  since  the  two  kinds  of  losses 
arise  from  entirely  different  causes,  it  is  necessary  to  consider  them 
separately  when  attempting  to  reduce  them  by  correct  methods  of  engine 
design. 

It  may  be  pointed  out  in  this  connection  that  while  it  is  possible  to 
measure  the  amount  of  leakage  while  an  engine  is  blocked  in  a  given 
position,  it  is  impossible  to  measure  or  to  estimate  the  leakage  which 
occurs  in  that  engine  under  operating  conditions.  If  an  engine  is  blocked 
in  position  and  steam  is  turned  on,  it  will  usually  be  found  that  no  important 
leak  takes  place  either  through  the  valves  or  past  the  piston.  If  the  valves 
of  this  engine  be  then  made  to  move  without  uncovering  the  ports,  they 
will  be  found  to  leak.  If  the  ports  of  a  slide  valve  engine  be  blocked  by 
some  means,  for  instance  by  filling  them  with  lead,  arid  the  valve  be 
made  to  move  in  the  normal  manner,  a  considerable  leak  will  usually  be 
discovered  from  the  steam  chest  into  the  exhaust  port.  A  part  of  this 
is  steam  leakage,  while  a  part  is  due  to  condensation  and  subsequent 
evaporation  of  the  steam  upon  the  valve  surface,  the  ports,  etcetera. 
Measuring  the  leakage  under  these  conditions  will  not,  however,  deter- 
mine the  leakage  under  normal  operating  conditions,  since  the  quality 
and  amount  of  steam  passing  through  the  valve  ports  is  radically  different. 

It  will  be  seen  that  the  automatic  engine  with  a  balanced  slide  valve 
is  essentially  wasteful,  on  account  of  this  source  of  loss.  This  is  one  reason 
for  its  rapid  displacement  of  late  years  by  the  four-valve  automatic  engine, 
in  which  this  source  of  loss  is  greatly  reduced,  if  not  entirely  obviated. 
There  is  no  possible  way  by  which  the  loss  due  to  leakage  in  a  Corliss  or 
other  four-valve  engine  can  be  measured,  but  it  is  probable  that  this 
loss  under  running  conditions  is  not  materially  greater  than  it  is  when 
the  engine  is  blocked  and  the  valves  are  closed. 

181.  Conduction  and  Radiation.  The  seventh  source  of  loss,  namely 
the  conduction  and  radiation  of  heat  from  the  steam  cylinder,  has  the 
effect  of  increasing  the  cylinder  condensation  by  reducing  the  mean  tem- 
perature of  the  cylinder  wall  and  thereby  increasing  the  temperature 
range  of  the  wall  surface.  Its  amount  in  the  case  of  a  jacketed  engine 
may  be  measured  by  determining  the  quantity  of  steam  condensed  in 
the  jacket  when  the  engine  is  not  running.  In  the  case  of  un jacketed 
engines  the  amount  of  this  loss  cannot  be  determined,  and  the  extent 
of  its  effect  upon  cylinder  condensation  is  impossible  of  estimation.  This 


ART.  183  LOSSES  DUE  TO   CLEARANCE  153 

source  of  loss  may  be  very  largely  eliminated  by  covering  the  exterior 
surface  of  the  cylinder  with  some  non-conducting  material,  such  as  mineral 
wool,  asbestos  sponge,  or  magnesia.  This  non-conducting  coating  is 
usually  covered  by  a  lagging  of  cast  iron  or  sheet  steel  for  the  purpose  of 
protecting  it  from  mechanical  injury  and  improving  the  appearance  of 
the  engine. 

182.  Losses  Due  to  Clearance.     It  has  already  been  shown  in  the 
preceding  chapter   that,  when  an  ideal  engine  has  clearance  no  thermo- 
dynamic  loss  results  if  the  expansion  and  the  compression  are  complete. 
In  the  case  of  a  practical  engine,  there  is  always  a  loss  due  to  clearance, 
even   though  both  the  expansion  and   compression  are  complete.     The 
work  of  compressing  the  cushion  steam  in  such  an  engine  is  much  greater 
than  the  work  done  by  the  cushion  steam  during  expansion,  since  the 
steam  is  practically  dry  and  saturated  at  the  beginning  of  compression, 
while  it  is  quite  wet  at  the  beginning  of  expansion,  on  account  of  initial 
condensation.     It  will  be  seen  that  the  amount  of  this  loss  depends  on 
the  weight  of  the  cushion  steam  and  can  be  reduced  only  by  reducing  the 
clearance   volume   and    the   compression    pressure    to   a   minimum.     In 
case  no  compression  is  employed  the  theoretical  efficiency  of  the  cycle 
will  be  reduced.     It  is  therefore  advisable  from  the  standpoint  of  efficiency 
to  adopt  that  degree  of  compression  which  will   make  the  sum  of  the 
theoretical  and  the  practical  losses  a  minimum.     The  greater  the  amount 
of  cylinder  condensation  the  greater  will  be  the  relative  importance  of  the 
practical  loss  and  the  less  the  degree  of  compression  which  may  be  profit- 
ably employed.     It  will,  therefore,  be  found  in  practice  that  compression 
is  undesirable  when  the  amount  of  cylinder  condensation  is  large. 

With  some  types  of  engines,  it  is  unadvisable  for  mechanical  reasons 
to  do  away  with  compression,  or  even  to  reduce  it  very  much.  This  is 
the  case  with  all  high-speed  engines.  A  considerable  amount  of  com- 
pression and  a  large  clearance  space  is  necessary  in  order  that  such  engines 
shall  operate  smoothly,  and  without  excessive  depreciation.  The  pur- 
pose of  the  cushion  steam  is  to  take  up  the  shock  which  would  otherwise 
be  experienced  as  a  result  of  the  rapid  reversal  of  the  heavy  reciprocat- 
ing parts  at  the  end  of  the  stroke.  High  speed  engines  are  necessarily 
made  with  large  clearance,  in  order  that  there  shall  be  sufficient  cushion 
steam  to  serve  this  purpose.  It  will  therefore  be  seen  that  the  clearance 
losses  are  high  in  this  type  of  engine,  and  it  is  partly  on  this  account 
that  the  slow-moving  long-stroke  engine  with  its  small  clearance  will 
usually  be  found  to  be  more  efficient. 

183.  Friction  Losses.     Usually  from  6  to  14  per  cent  of  the  power 
developed  in  the  cylinder  of  an  engine  at  rated  load  is  lost  in  overcoming 
the  friction  of  the  moving  parts.     The  amount  of  this  loss  varies  with 
the  speed  of  the  engine,  but  is  practically  independent  of  the  load.     Con- 


154 


LOSSES  IN  THE  STEAM   ENGINE 


ART.  183 


sequently,  the  indicated  power  developed  when  the  engine  is  running- 
idle  measures  the  amount  of  this  loss.  This  loss  may  be  minimized  by 
the  proper  design  and  lubrication  of  the  bearings  and  by  careful  attention 
to  their  adjustment  arid  alignment.  The  amount  of  the  loss  depends  upon 
the  weight  of  the  moving  parts,  the  relative  velocity  of  the  rubbing  sur- 
faces, the  quality  of  the  lubricant,  the  method  of  introducing  the  lubricant, 
the  fit -of  the  bearings,  and  the  ratio  of  the  maximum  to  the  mean  effective 
pressure.  Heavy  moving  parts,  by  increasing  the  pressure  on  the  bearings, 
increase  the  friction  loss.  When  the  shafts  and  pins  are  larger  in  diameter 
than  is  necessary  for  proper  strength  and  stiffness,  the  friction  loss  is 
increased  on  account  of  the  higher  velocity  of  rubbing.  When  a  copious 
supply  of  good  lubricant  is  furnished  in  such  a  manner  that  it  completely 
lubricates  the  rubbing  surfaces,  the  loss  is  reduced.  The  most  efficient 
method  of  accomplishing  this  is  to  furnish  an  excess  of  the  lubricant  at 
the  points  where  the  bearing  pressure  is  the  greatest,  by  means  of  a 
force  pump,  so  that  the  shaft  is  practically  floated  on  oil.  When  the  sup- 


FIG.  75  a.  FIG.  75  6. 

Showing  the  effect  of  excessive  running  clearance. 

ply  of  oil  is  insufficient  the  lubricating  film  between  the  rubbing  surfaces 
is  thin.  The  amount  of  friction  loss  varies  inversely  with  trie  thickness 
of  this  film,  hence  the  desirability  of  an  ample  supply  of  lubricant.  The 
difference  between  the  diameter  of  the  shaft  or  pin,  and  of  the  box  in 
which  it  rotates,  is  an  important  matter.  If  the  difference  is  too  small, 
the  lubricating  film  is  necessarily  thin,  and  the  friction  loss  high.  If 
the  difference  is  too  great,  the  shaft  will  be  supported  in  the  manner  shown 
in  Fig.  75  a,  instead  of  that  shown  in  Fig.  75  6,  and  the  lubricating  film 
will  be  easily  destroyed  on  account  of  the  excessive  pressure  along  the 
narrow  surface  of  contact  at  c. 

When  the  ratio  of  the  maximum  to  the  mean  effective  pressure  is 
high,  not  only  must  the  moving  parts  be  heavy  in  order  to  resist  the 
excessive  stresses  imposed  at  certain  parts  of  the  stroke,  but  the  pres- 
sure transmitted  from  the  piston  to  the  bearings  will  be  large  in  comparison 
with  the  power  actually  developed.  A  low  ratio  of  expansion  is  there- 
fore favorable  to  high  mechanical  efficiency.  The  mechanical  efficiency 
of  a  compound  engine  will  be  higher  than  that  of  a  simple  engine  having 


ART.  184 


REDUCING   THE   LOSSES   BY   PROPER   DESIGN 


155 


the  same  total  expansion,  since  the  expansion  is  divided  between  two 
cylinders  in  the  case  of  a  compound  engine,  and  the  ratio  of  the  maximum 
to  the  mean  effective  pressure  is  greatly  reduced.  By  increasing  the 
number  of  cylinders  acting  upon  a  shaft,  the  turning  moment  is  made 
more  even,  and  the  weight  of  the  fly-wheel  may  be  reduced.  A  cross 
compound  engine  in  which  two  cylinders  act  on  crank  pins  set  at  right 
angles  is  therefore  more  efficient  mechanically  than  a  single  cylinder 
engine  or  a  tandem  compound  engine  of  the  same  power  and  speed. 

Since  the  fly-wheel  and  other  moving  parts  of  a  high  speed  engine 
are  usually  much  lighter  than  those  of  a  long  stroke  engine  of  the  same 
power,  and  since  the  ratio  of  expansion  is  greater  in  the  case  of  a  long 
stroke  engine,  a  high  speed  engine  is  usually  mechanically  more  efficient 
than  a  long  stroke  engine.  A  few  tests  are  on  record  which  indicate  an 
exceedingly  small  loss  from  mechanical  friction  in  high  speed  engines, 
sometimes  as  low  as  2  per  cent  of  the  indicated  horse-power  of  the  engine, 
but  it  is  doubtful  whether  these  unusual  results  were  realized,  or  whether 
the  tests  were  inaccurate. 

184.  Reducing  the  Losses  by  Proper  Design.  It  will  be  noted  that 
some  of  these  losses  are  of  such  a  nature  that  when  one  is  decreased, 
another  one  is  increased.  It  slhould  be  the  aim  of  the  engine  designer 
to  reduce  the  sum  of  the  losses  to  a  minimum,  which  involves  balancing 
these  losses  one  against  another.  For  instance,  increasing  the  ratio 
of  expansion  reduces  the  loss  due  to  the  imperfection  of  the  cycle  and 
increases  that  due  to  cylin- 
der condensation.  For  some  10 
particular  ratio  of  expan- 
sion, the  sum  of  these  two 
losses  will  be  a  minimum, 
and  that  ratio  of  expansion 
will  be  the  one  chosen. 

The  design  of  an  engine, 
however,  is  not  an  exact 
process  in  which  the  various 
losses  are  exactly  estimated 
and  balanced  one  against 
another,  and  certain  dimen- 
sions accurately  determined 
which  will  make  the  sum 

of  these  losses  a  minimum.  On  the  contrary,  a  considerable  latitude 
may  be  allowed  in  fixing  upon  the  principal  dimensions  of  an  engine 
without  affecting  its  efficiency  to  any  noticable  degree.  In  Fig.  76 
will  be  found  a  curve  giving  the  relation  of  the  ratio  of  expansion  occurring 
in  an  actual  engine  to  the  efficiency  of  the  engine.  It  will  be  seen  that 


456 
Ratio  of  Expansion 

FIG.  76. — Effect  of   changing   the  ratio   of  expan- 
sion on  the  efficiency  of  an  engine. 


156  LOSSES  IN  THE  STEAM   ENGINE  ART.  184 

as  the  ratio  of  expansion  is  increased  the  efficiency  rises  and  then  falls 
off,  and  that  for  the  ratio  of  expansion  between  2f  and  4,  the  efficiency 
is  practically  constant.  Similar  effects  may  be  noticed  in  regard  to  changes 
in  almost  every  one  of  the  principal  dimensions  of  an  engine. 

Not  all  of  the  sources  of  loss  are  of  this  character,  however.  Increasing 
the  clearance  volume  of  an  engine,  for  instance,  always  reduces  the 
efficiency  of  the  engine.  Increasing  the  clearance  area  invariably  has 
the  same  effect.  In  cases  of  this  kind,  it  should  be  the  aim  of  the  designer 
to  adopt  every  expedient  which  will  reduce  such  losses  to  a  minimum. 

PROBLEMS 

1.  What  per  cent  of  the  heat  supplied  is  unavoidably  lost  with  the  perfect  cycle 
when  steam  is  supplied  at  100   Ibs.,  absolute   and   exhausted   at    a  pressure  of   one 
atmosphere?  .  Ans.     15  per  cent. 

2.  What  per  cent  is  unavoidably  lost  when  steam  is  supplied  at  180  Ibs.  absolute 
and  a  superheat  of  200°  and  the  final  temperature  of  the  condensing  water  is  90°  F.? 

Ans.     53.2  per  cent. 

3.  If  the  theoretical  efficiency  of  the  cycle  employed  in  the  first  case  is  10  per  cent, 
what  per  cent  of  the  available  heat  is  lost?  Ans.     33  per  cent. 

4.  A  Rankine  cycle  is  employed  in  Problem  2.      What  per  cent  of  the  available 
heat  is  lost?  Ans.     33.4  per  cent. 

5.  If  the  back  pressure  in  the  engine  in  Problem  4  be  1.5  Ibs.  instead  of  that  cor- 
responding to  the  temperature  of  the  discharged  condensing  water,  what  per  cent  of 
power  will  be  lost,  assuming  a  Rankine  cycle  to  be  employed  between  the  new  pressure 
limits?  Ans.     8  per  cent. 

6.  The  mean  effective  pressure  of  an  actual  indicator  card  is  45  Ibs.     The  theoretical 
mean  effective  pressure  for  the  same  ratio  of  expansion,  back  pressure,  and  amount  of 
compression,. is  48  Ibs.    What  is  the  card  factor  of  the  engine?          Ans.     94  per  cent. 

7.  The  mean  effective  pressure  obtained  from  the  theoretical  indicator  card  for  a 
locomotive  is  126  Ibs.     What  will  be  probable  actual  mean  effective  pressure? 

Ans.     94  to  106  Ibs. 

8.  An  engine  cylinder  is  10  in.  in  diameter  and  the  area  of  the  ports  is  8  sq.  ins. 
The  mean  piston  speed  is  600  ft.  per  minute.      What  is  the  nominal  velocity  of  the 
steam?  Ans.     5,850  ft.  per  minute. 

9.  An  engine  having  a  cylinder  18  ins.  in  diameter  and  a  3-ft.  stroke,  makes  125 
revolutions  per  minute.     Assuming  a  nonrnal  steam  velocity  of  5,000  ft.  per  minute, 
what  will  be  the  area  of  the  exhaust  ports?  Ans.     38  sq.  in. 

10.  A  non-condensing  engine  takes  steam  at  a  pressure  of  100  Ibs.  absolute  and 
has  a  ratio  of  expansion  of  3.    The  area  of  wall  surface  exposed  to  the  action  of  the 
steam  per  revolution  at  cut-off  is  10  sq.  ft.  and  the  number  of  revolutions  per  minute 
is  200.    Find  the  weight  of  steam  condensed  per  revolution.  Ans.     1.0276  Ibs. 

11.  The  low  pressure  piston  of  a  triple  expansion  engine  is  provided  with  poppet 
valves,  so  that  the  area  of  wall  surface  exposed  to  the  action  of  steam  at  cut-off  is  that 
of  the  cylinder  head,  piston,  and  the  barrel.     The  initial  pressure  is  14  Ibs.  absolute 
and  the  condenser  pressure  1  Ib.  absolute.     The  cylinder  is  80  ins.  in  diameter  and  5  ft. 
stroke.     The  engine  makes  30  revolutions  per  minute.     The  ratio  of  expansion  is  2. 
Find  the  weight  of  steam  condensed  per  revolution  in  per  cert  of  the  cylinder  feed  per 
revolution,  assuming  no  clearance  volume.  Ans.     35  per  cent. 


ART.  184  PROBLEMS  157 

12.  Construct  an  indicator  card  for  an  engine  taking  steam  at  100  Ibs.  absolute 
and  discharging  it  at  16  Ibs.  absolute  with  a  ratio  of  expansion  of  3,  having  10  per  cent 
clearance  and  complete  compression,  assuming  all  compression  and  expansion  lines 
to  be  hyperbolic,  and  that  the  quality  of  the  steam  in  the  cylinder  at  cut-off  is  50  per 
cent  and  at  compression  100  per  cent.      Find  the  work  done  per  pound  of  working 
fluid. 

13.  Find  the  work  done  per  pound  of  steam  supplied. 

14.  Assume  the  same  conditions  as  before  except  that  there  is  no  compression, 
and  find  the  work  done  per  pound  of  working  fluid. 

15.  Find  the  work  done  per  pound  of  steam  supplied.     (Note  the  effect  of  com- 
pression on  the  efficiency.) 

16.  A  friction  card  is  taken  from  an  engine  and  its  area  found  to  be  0.16  sq.  in. 
The  card  at  full  load  of  the  same  length  has  an  area  of  1.55  sq.  ins.      What  is  the 

mechanical  efficiency  of  the  engine?  Ans.     89.7  per  cent. 


CHAPTER  XI 
NOTES  ON  THE  DESIGN  AND  TESTING  OF  STEAM  ENGINES 

185.  Choice  of  Type  of  Engine.  In  designing  a  steam  engine,  it  is 
first  necessary  to  settle  upon  the  type  of  engine  and  the  range  of  .steam 
pressure  to  be  employed.  The  type  chosen  will  depend  upon  the  power 
required,  and  upon  the  use  to  which  the  engine  is  to  be  put,  and  is  settled 
primarily  by  financial  and  not  by  purely  thermodynamic  considerations. 
It  is  desirable  that  the  cost  of  operation  of  the  power  plant  shall  be  a 
minimum.  This  cost  of  operation  includes  three  principal  elements, 
the  first  being  the  cost  of  fuel,  the  second  the  cost  of  attendance,  and  the 
third  the  interest  and  other  fixed  charges  on  the  first  cost  of  the  plant. 
An  engine  which  is  highly  economical  in  the  use  of  fuel  usually  will  be 
costly,  and  hence  the  fixed  charges  will  be  large.  If  an  engine  is  to  be 
operated  for  a  large  part  of  the  time,  or  if  fuel  is  expensive,  the  cost  of 
the  fuel  becomes  the  most  important  element  in  the  cost  of  operation, 
and  a  highly  efficient  type  of  engine  will  be  chosen,  in  spite  of  its  first 
cost.  If  the  engine  is  to  be  used  only  a  small  part  of  the  time,  or  if  it 
is  small  in  size,  or  if  the  fuel  is  cheap,  the  fixed  charges  become  the  largest 
item  in  the  cost  of  operation.  In  such  a  case  the  cheapest  engine  will 
be  chosen  in  spite  of  its  low  efficiency. 

In  this  connection  it  should  be  remembered  that  it  is  not  the  cost  of 
the  engine  alone,  but  the  cost  of  the  whole  plant  which  we  desire  to  reduce. 
The  more  efficient  the  engine,  the  smaller  the  boiler  which  will  be  required 
to  operate  it.  If  a  cheap  engine  is  very  inefficient,  the  boiler  required 
may  become  so  large  and  costly  that  the  total  cost  of  the  plant  will  be 
greater  than  it  would  be  if  a  more  costly,  but  more  efficient  engine  had  been 
chosen.  Hence,  when  comparing  the  cost  of  operation  of  two  engines, 
it  is  necessary  to  take  account  of  the  size  and  cost  of  the  boiler  plant 
required  to  operate  each  of  them. 

It  is  not  often,  however,  that  the  designer  of  an  engine  is  called  upon 
to  fix  the  type  and  horse-power  of  the  engine,  or  the  range  of  steam 
pressure  to  be  employed.  That  is  usually  the  work  of  the  consulting- 
engineer  who  designs  the  power  plant.  While  large  engines  are  almost 
always  built  to  order,  they  are  usually  built  from  standard  drawings  and 
patterns,  which  have  been  prepared  in  anticipation  of  the  probable  require- 
ments of  power  plant  engineers.  When  a  number  of  such  designs  have 

158 


ART.  186  MULTIPLE  EXPANSION   ENGINES  159 

been  submitted  to  him,  together  with  the  prices  of  the  engines,  it  is  the 
duty  of  the  consulting  engineer  to  choose  the  particular  one  which  will 
give  the  lowest  plant  operating  cost.  The  type  and  size  of  engine  which 
a  manufacturer  will  attempt  to  build  will  depend  on  the  facilities  of 
his  plant,  and  the  apparent  demands  of  the  market.  Having  originated 
a  series  of  sizes,  he  will  then,  by  making  minor  changes  in  his  designs  and 
patterns,  seek  to  adapt  them  in  the  best  manner  possible  to  the  needs 
of  each  particular  case,  as  they  are  outlined  by  the  consulting 
engineer. 

186.  Cylinder  Arrangements  for  Multiple  Expansion  Engines.  The 
multiple  expansion  engine  is  an  engine  in  which  the  steam  performs 
work  in  two  or  more  cylinders  in  succession,  in  the  manner  already  described 
in  Chapter  VIII,  Art.  128.  Many  different  cylinder  arrangements  are 
used  for  such  engines.  In  the  case  of  compound  engines,  the  two  cylin- 
ders may  be  in  line  with  one  another  with  the  two  pistons  upon  a  com- 
mon piston  rod  as  in  Fig.  77  a.  The  first  cylinder  into  which  the  steam 
enters  is  called  the  high  pressure  cylinder,  while  the  second  is  called  the 
low  pressure  cylinder.  They  are  indicated  by  the  letters  H.P.  and  L.P. 
in  the  diagram.  Rec.  is  the  receiver  placed  between  the  cylinders.  This 
arrangement  is  termed  a  tandem  compound  engine.  A  second  arrange- 
ment is  shown  in  Fig.  77  fr,  and  is  known  as  a  cross  compound  engine. 
The  two  cylinders  are  side  by  side,  each  one  acting  upon  a  separate  crank, 
which  is  keyed  to  a  common  shaft.  In  order  to  obtain  a  more  even  turn- 
ing moment  the  two  cranks  are  placed  at  right  angles  to  one  another, 
so  that  when  one  of  the  cylinders  is  at  dead  center,  the  other  one  will 
be  at  mid-stroke.  A  compound  engine  may  have  two  L.P.  cylinders, 
in  which  case  it  is  called  a  three-cylinder  compound.  The  cylinders 
are  then  usually  arranged  side  by  side,  and  act  upon  three  separate  cranks 
set  at  120°  to  each  other,  all  keyed  to  a  common  shaft  as  shown  in  Fig. 
77  c.  A  fourth  arrangement  is  that  known  as  the  angle  compound  engine 
shown  in  Fig.  77  d,  in  which  one  cylinder  (usually  the  H.P.)  is  horizontal, 
and  the  other  is  vertical.  Both  act  on  a  common  crank  pin,  and  since 
one  cylinder  is  at  dead  center  while  the  other  is  at  mid-stroke,  the  same 
uniform  turning  moment  is  obtained  as  is  gotten  from  a  cross  compound 
engine. 

A  fifth  arrangement  is  that  termed  the  duplex  compound,  in  which 
the  H.P.  and  L.P.  cylinders  both  act  on  a  common  cross-head,  as  shown 
in  Fig.  77  e.  A  sixth  arrangement,  which  permits  the  designer  to  dis- 
pense with  the  receiver,  is  termed  a  Wolff  compound,  and  is  illustrated 
in  Fig.  77  /.  The  two  cross-heads  are  linked  to  opposite  ends  of  a  walk- 
ing-beam, so  that  the  two  pistons  move  in  opposite  directions.  Admis- 
sion to  the  L.P.  cylinder  occurs  directly  through  the  exhaust  valve  of 
the  H.P.  cylinder,  and  continues  for  almost  the  entire  stroke.  Various 


160      NOTES   ON  DESIGN  AND   TESTING  OF   STEAM  ENGINES    ART.  186 


ART.  186 


MULTIPLE  EXPANSION    ENGINES 


161 


other  cylinder  arrangements  are  occasionally  used  in  practice,  but  the 
ones  given  are  the  most  common. 

The  triple  expansion  engine  usually  has  three  cylinders,  termed  respect- 
ively the  high  pressure,  the  intermediate,  and  the  low  pressure  cylinders. 
The  two  receivers  are  known  as  the  first  and  second  receivers.  The  three 
cylinders  are  usually  placed  side  by  side  and  act  on  three  cranks  keyed 
to  a  common  shaft  and  placed  at  angles  of  120°  with  one  another,  as  shown 
in  Fig.  78  a.  Four  cylinder  triple  expansion  engines  are  often  built, 


H.P. 


I.P. 


L.P. 


v 


1 


IL 


FIG.  78  a 


n 


FIG.  78  6 
FIG.  78. — Cylinder  arrangements  for  triple  expansion  engines. 

having  two  low  pressure  cylinders.  They  are  arranged  as  shown  in  Fig. 
78  6.  Quadruple  expansion  engines  are  seldom  built  except  for  merchant 
marine  service,  and  often  have  5  or  6  cylinders,  acting  on  as  many  cranks 
keyed  to  a  common  shaft.  The  introduction  of  the  steam  jturbine  which 
is  capable  of  utilizing  low  pressure  steam  to  better  advantage  than  the 
steam  engine  has  tended  to  minimize  the  importance  of  triple  and  quad- 
ruple expansion  engines.  Greater  economy  can  be  obtained  by  utilizing 


162        NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES     ART.  187 

the  steam  from  a  compound  engine  in  a  low  pressure  steam  turbine  than 
by  further  expanding  it  in  additional  cylinders. 

187.  Advantages   of    Multiple  Expansion.     The    multiple   expansion 
engine  offers  several  advantages  over  a  single  engine  having  the  same 
ratio  of  expansion.     They  are: 

First,  reduced  cylinder  condensation,  on  account  of  the  reduction 
in  the  temperature  range  and  ratio  of  expansion  per  cylinder. 

Second,  reduced  leakage  loss,  on  account  of  a  reduction  in  the  pres- 
sure difference  which  causes  the  leakage.  • 

Third,  higher  mechanical  efficiency,  since  the  ratio  of  the  maximum 
to  the  mean  effective  pressure  in  each  of  the  cylinders  is  greatly 
reduced,  being  usually  from  40  to  70  per  cent  of  what  it  would  be 
were  the  same  total  ratio  of  expansion  employed  in  a  single  cylinder 
engine. 

Fourth,  the  principal  parts  of  the  engine  are  less  heavy  and  costly, 
since  the  maximum  total  steam  pressure  on  each  of  the  pistons  is  only 
from  20  to  30  per  cent  of  what  it  would  be  were  a  single  cylinder  engine 
employed  having  the  same  total  ratio  of  expansion. 

Fifth,  by  causing  two  or  more  cylinders  to  operate  on  separate  cranks 
on  the  same  shaft,  as  is  done  in  the  cross  compound  engine,  a  more  even 
turning  moment  may  be  secured,  which  is  a  matter  of  very  great  importance 
in  the  case  of  engines  operating  alternating  current  generators  in  parallel, 
and  is  desirable  in  many  other  cases. 

188.  Action  of  the  Steam  in  a  Compound  Engine.     In  order  to  make 
clear  the  action  of  the  steam  in  the  cylinders  of  a  compound  engine,  the 
simplest  possible  case  will  be  considered.     Assume  a  compound  engine 
in  which  the  weight  of  cushion  steam  is  the  same  per  stroke  for  each 
cylinder;  the  H.P.  cylinder  is  without  compression,  and  the  L.P.  cylinder 
has  complete  compression.     The  weight  of  cylinder  feed  per  stroke  will 
of  course  be  the  same  for  each  cylinder,  since  all  of  the  steam  leaving  the 
high  pressure  cylinder  must  pass  through  the  low  pressure  cylinder  before 
it  is  finally  discharged  from  the  engine.     Assume  that  the  receiver  is  of 
very  large  volume,  so  that  no  change  of  pressure  results  when  the  H.P. 
cylnder  is  discharged  into  it  or  the  L.P.  cylinder  takes  steam  from  it.     If 
there  is  no  loss  from  wire  drawing  the  pressure  of  the  steam   entering 
the  L.P.  cylinder  will  be  the  same  as  that  exhausted  from  the  H.P.  cyl- 
inder.    If  the  volume  of  the  steam  taken  per  stroke  by  the  L.P.  cylinder 
is  the  same  as  the  volume  of  the  steam  discharged  by  the  H.P.  cylinder, 
the  H.P.  cylinder  will  have  complete  expansion  and  the  form  of  its  card 
will  be  that  bounded  by  the  lines  ab  c  din  Fig.  79.     The  L.P.  cylinder  will 
take  the  same  volume  of  steam  from  the  receiver  as  was  discharged  into 
it  by  the  H.P.  cylinder,  and  its  card  will  be   that  bounded  by  the  lines 
dcefg  in  the  same  figure.     An  inspection  of  the  two  cards  will   serve 


ART.  189        DETERMINATION   OF   CYLINDER   DIMENSIONS 


163 


G 


F 


FIG.  79. — Theoretical  card  for  a  com- 
pound engine. 


to  show  that  they  are  simply  the  theoretical  card  of  an  engine  having  a 
large  ratio  of  expansion. 

The  work  done  by  the  steam  in  passing  through  the  engine  is  the  same 
as  the  work  which  that  steam  would  do  in  the  L.P.  cylinder  of  the  engine, 
if  the  steam  were  admitted  to  the 
cylinder  at  boiler  pressure,  and  a 
sufficiently  short  cut-off  were  used  to 
get  the  same  ratio  of  expansion  in 
the  L.P.  cylinder  as  actually  occurs 
in  the  entire  engine.  The  addition 
of  the  high  pressure  cylinder  does 
not  increase  the  power  of  the  engine, 
but  it  does  result  in  gaining  the 
advantages  already  enumerated  in 
the  preceding  article.  On  this  ac- 
count, when  the  range  of  steam 
pressure  available  is  great  enough 

to  make  a  large  ratio  of  expansion  desirable,    a    compound    engine    is 
almost  always  chosen,  rather  than  a  simple  engine  of  the  same  power. 

It  is  not  often,  however,  that  the  clearance  volumes  and  points  of 
compression  in  the  high  and  low  pressure  cylinders  of  an  engine  are  so 
adjusted  that  the  weight  of  cushion  steam  contained  in  each  cylinder  is 
the  same.  Furthermore,  the  receiver  is  never  of  sufficiently  large  volume 
to  eliminate  pressure  changes  due  to  the  discharge  of  steam  by  the  H.P. 
cylinder  and  draft  of  steam  by  the  L.P.  cylinder.  On  this  account, 
the  usual  behavior  of  the  steam  in  the  cylinders  of  a  multiple  expansion 
engine  is  not  quite  the  simple  matter  that  has  been  outlined.  However, 
the  error  introduced  by  estimating  the  power  of  a  multiple  expansion 
engine  from  the  area  of  the  theoretical  card  already  described  and  the 
volume  of  its  low  pressure  cylinder,  is  so  small  that  it  may  be  neglected 
in  designing  such  an  engine.  It  is  customary  in  design  work  to  fix  the 
size  of  the  low  pressure  cylinder  of  a  multiple  expansion  engine  by  assum- 
ing that  steam  is  admitted  to  that  cylinder  at  boiler  pressure,  and  that 
the  total  range  of  expansion  occurs  there. 

189.  Determination  of  Cylinder  Dimensions.  When  the  size  and 
type  of  engine  and  range  of  steam  pressure  have  been  settled,  either 
to  meet  a  given  set  of  operating  conditions  or  to  meet  the  probable  require- 
ments of  the  market,  it  is  next  in  order  to  determine  the  probable  mean 
effective  pressure  and  the  size  of  cylinder  (or  in  the  case  of  a  multiple 
expansion  engine,  the  size  of  L.P.  cylinder)  required  to  develop  the 
power.  In  order  to  do  this,  it  is  usual  to  lay  out  to  scale  the  theoretical 
card  for  the  pressure  range  and  ratio  of  expansion  which  it  has  been 
decided  to  adopt.  Having  drawn  the  theoretical  card,  the  designer 


164     NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES  ART.  189 

measures  or  calculates  its  area  and  from  its  area  and  length  the  mean 
ordinate  of  the  card  is  obtained.  Multiplying  together  the  height  of  the 
mean  ordinate,  and  the  pressure  scale  of  the  drawing,  the  theoretical 
mean  effective  pressure  is  obtained.  The  theoretical  mean  effective 
pressure  should  then  be  multiplied  by  the  proper  card  factor  in  order  to 
obtain  the  actual  mean  effective  pressure  at  the  rated  load  of  the  engine. 
The  area  of  the  piston  of  the  engine  is  now  obtained  by  the  formula 

A  =33,000™, 

in  which  A  is  the  area  of  the  piston  in  square  inches,  HP  is  the  indicated 
horse-power  of  the  engine  at  rated  load,  S  is  the  mean  piston  speed  in 
feet  per  minute,  and  P  is  the  mean  effective  pressure  in  pounds  per  square 
inch.  The  mean  piston  speed  is  of  course  equal  to  twice  the  length  of 
the  stroke  in  feet  times  the  number  of  revolutions  per  minute.  The  area 
so  obtained  will  of  course,  be  the  area  of  the  low  pressure  piston  in  the 
case  of  a  multiple  expansion  engine.  In  case  the  engine  has  two  or  more 
L.P.  cylinders,  it  is  the  combined  area  of  all  the  L.P.  pistons. 

If  the  engine  is  to  be  a  compound  or  triple  expansion  engine,  the 
theoretical  card  is  now  divided  by  horizontal  lines  into  two  or  three  por- 
tions as  nearly  equal  in  area  as  may  be.  This  is  done  in  order  that  the 
amount  of  work  developed  in  each  of  the  cylinders  shall  be  the  same. 
Fig.  SO  represents  such  a  card  as  would  be  laid  out  in  designing  a  com- 
pound engine.  The  horizontal  line 
e  f  divides  the  card  into  two  portions 
of  nearly  equal  area.  The  high 
pressure  card  which  is  the  upper  of 
the  two  areas  is  now  modified  by 
giving  a  certain  amount  of  terminal 
drop  as  shown  by  the  line  c  d.  The 
reasons  for  giving  this  terminal 
drop  are  that  it  reduces  the  size  of 
the  high  pressure  cylinder,  increases 


FIG.  80.— Card  used  in  designing  a        the     mechanical     efficiency    of     the 
compound  engine.  engine,  and  reduces  the  loss  due   to 

cylinder   condensation.     The    length 

e  d  will  now  represent  the  swept  volume  of  the  H.P.  cylinder  while 
the  length  i  h  will  represent  the  swept  volume  of  the  low  pressure 
cylinder.  If  both  cylinders  are  of  the  same  length  of  stroke,  the 
ratio  of  e  d  to  i  h  also  represents  the  ratio  of  the  piston  areas  of  the 
two  cylinders.  Having  determined  the  area  of  the  low  pressure  piston 
by  the  rule  already  given,  the  area  of  the  high  pressure  piston  may  bo 
determined  by  this  ratio.  The  length  of  stroke  may  next  be  chosen, 


ART.  190  THE  DESIGN  OF  RECEIVERS  165 

and  the  number  of  revolutions  per  minute  be  determined  by  twice  the 
length  of  stroke  in  feet. 

190.  The  Design  of  Receivers.  In  order  that  the  low  pressure  cylin- 
der may  receive  its  supply  of  steam  without  too  much  variation  in  pres- 
sure, and  that  the  high  pressure  cylinder  may  exhaust  its  steam,  while 
the  low  pressure  inlet  valves  are  closed,  a  receiver  of  considerable  vol- 
ume is  interposed  between  the  high  and  low  pressure  cylinders.  The 
volume  of  the  receiver  is  usually  made  from  2  to  6  times  the  volume 
of  the  high  pressure  cylinder.  The  larger  the  volume  of  this  receiver, 
the  higher  the  card  factor  of  the  engine,  and  the  less  the  loss  due  to  over- 
lapping of  the  cards.  However,  if  the  receiver  is  made  too  large,  the 
loss  due  to  radiation  will  overcome  the  advantage  of  an  improved  card 
factor,  so  that  the  limits  given  represented  the  practical  range  in  varia- 
tion of  receiver  volume.  In  the  case  of  a  triple  expansion  engine,  the 
volume  of  the  second  receiver,  interposed  between  the  intermediate  and 
low  pressure  cylinders,  is  from  1^  to  4  times  that  of  the  intermediate 
cylinders.  It  may  be  shown  that  the  relative  position  of  the  cranks 
of  an  engine  has  an  important  effect  on  the  range  of  pressure  variation 
in  the  receiver.  The  cranks  should  be  so  placed  that  this  pressure  varia- 
tion will  be  a  minimum. 

On  account  of  its  adiabatic  expansion  and  the  loss  of  heat  by  radia- 
tion, the  steam  which  enters  the  receiver  will  be  wet.  If  this  wet  steam 
is  permitted  to  enter  the  low  pressure  cylinder,  the  cylinder  condensa- 
tion will  be  greatly  increased  on  account  of  the  excessive  wetness  of  the 
steam.  To  avoid  this  it  is  customary  to  heat  the  steam  in  the  receiver 
by  means  of  a  coil  of  pipe  called  a  reheater.  The  reheater  is  supplied 
with  steam  of  a  higher  pressure  than  that  in  the  receiver,  and  on  account 
of  its  high  temperature  it  evaporates  the  water,  thus  supplying  the  second 
cylinder  with  dry  steam.  However,  this  action  is  accompanied  by  a 
thermodynamic  loss  and  is  practically  the  equivalent  of  operating  the 
engine  on  a  jacketed  cycle.  A  preferable  method  is  to  so  form  the  receiver 
-  that  it  becones  a  separator,  mechanically  removing  the  moisture  con- 
tained in  the  entering  steam,  and  supplying  the  second  cylinder  with 
steam  that  is  practically  dry.  A  reheater  may  be  used  to  advantage  in 
connection  with  a  separating  receiver,  but  the  amount  of  heat  supplied 
by  the  reheater  will  then  be  very  small.  The  use  of  the  reheater  will 
give  almost  absolutely  dry  steam  to  the  following  cylinder,  with  a  result- 
ing decrease  in  the  loss  from  cylinder  condensation. 

The  amount  of  reheater  surface  used  varies  greatly  in  different  types 
of  engines,  and  is  dependent  very  largely  on  the  judgment  of  the  designer. 
Good  practice  sanctions  the  use  of  from  0.02  to  0.05  square  feet  of  reheat- 
ing surface  per  pound  of  steam  per  hour.  In  case  a  separating  receiver 
is  used,  the  area  of  reheating  surface  may,  of  course,  be  greatly  diminished. 


166     NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES     ART.  19' 

191.  Design  of  Jackets.     In  the  case  of  very  slow-moving  engines,  as 
for  instance  long  stroke  pumping  engines,  the  cylinders  should  be  jacketed. 
It  is  customary,  when  practicable,  to  jacket  both  the  barrel  and  the 
heads  of  the   cylinder.      It  is  equally  advisable   to  jacket  the  piston 
although  this  is  seldom  attempted  on  account  of  the  difficulty  of  intn;v 
ducing  steam  and  carrying  away  the  drip  through  the  piston  rod.     When 
jacketing  an  engine,  care  must  be  taken  that  the  jackets  are  drained, 
so  that  water  will  not  accumulate  in  them,  since  a  jacket  filled  with  water 
tends  to  increase  rather  than  diminish  the  loss  due  to  cylinder  condensa- 
tion.    It  is  not  difficult  to  drain  the  jackets  of  the  cylinder  barrel,  but  oft- 
times  considerable  ingenuity  must  be  used  in  order  to  drain  the  jackets 
of  the  heads,  when  the  valves  are  placed  in  the  heads,  as  they  are  usually 
in  the  case  of  slow  speed  vertical  engines.     The  reheating  coils  in  the 
receivers  must  also  be  so  arranged  that  they  can  be  drained.     The  jacket 
drain  should  lead  to  a  trap  which  will  discharge  the  accumulated  water 
without  permitting  the  escape  of  steam.     In  the  case  of  a  high  pressure 
cylinder,  this  trap  should  discharge  into  the  receiver,  as  should  also  the 
drip  from  the  reheating  coil,  in  order  that  the  sensible  heat  of  the  water 
may  be  utilized  in  evaporating  a  portion  of  its  weight  into  steam,  which 
will  do  work  in  the  low  pressure  cylinder.     In  a  triple  expansion  engine, 
the  drips  from  the  intermediate  cylinder  and  the  reheater  coil  of  the  second 
receiver  in  like  manner  may  discharge  into  the  second  receiver. 

When  a  highly  efficient  multiple  expansion  engine  is  desired,  an 
approximation  to  the  Carnot  cycle  may  be  obtained  by  pumping  the  feed- 
water  from  the  hot  well  (i.e.,  the  chamber  into  which  the  air-pump  dis- 
charges the  condensed  steam)  through  heating  coils  surrounded  by  steam 
from  the  receivers.  The  steam  used  to  heat  the  feed- water  has  already 
done  work  in  one  or  more  cylinders,  and  the  feed-water  is  finally  sup- 
plied to  the  boiler  at  practically  the  temperature  of  the  steam  in  the  first 
receiver.  While  this  method  makes  an  engine  highly  economical,  the 
economy  of  the  plant  will  be  lower  than  if  an  economizer  were  used. 
Although  this  method  has  been  employed  in  practice,  it  was  used,  not  in 
order  to  secure  a  high  plant  economy,  but  in  order  to  earn  a  bonus  for  a 
high  engine  economy. 

Having  settled  upon  the  areas  of  the  pistons,  the  length  of  stroke, 
the  number  of  revolutions  per  minute  of  the  engine,  the  volume  of  the 
receivers  and  the  amount  of  reheating  surface,  the  areas  of  the  ports 
may  be  computed  by  the  rules  given  in  Art.  170.  The  remainder  of  the 
design  of  the  engine  becomes  a  problem  in  machine  design  in  which  the 
principles  of  thermodynamics  play  no  part. 

192.  Theoretical  Indicator  Cards  for  Multiple  Expansion  Engines.      Iri 

order  to  construct  accurately  the  theoretical  indicator  cards  for  a  multiple  expansion 
engine,  it  is  necessary  to  take  account  of  the  volume  of  the  receivers,  and  the  pressure 


VRT.  192     INDICATOR  CARDS  FOR  MULTIPLE  EXPANSION  ENGINES     167 


variations  which  take  place  within  them.  It  is  customary  to  compute  the  form  of 
the  cards  for  such  engines  on  the  assumption  that  the  product  of  the  pressure  and  the 
volume  of  a  given  weight  of  steam  is  a  constant  quantity.  This  is  not  exactly  true, 
but  is  a  sufficient  approximation  in  estimating  the  power  and  proportioning  the  cylin- 
ders of  such  engines.  Having  designed  the  cylinders  and  the  receivers  of  a  multiple 
xpansion  engine,  and,  from  the  design,  computed  the  clearance  volume  of  each  of  the 
cylinders,  we  are  in  position  to  draw  the  theoretical  indicator  cards  of  the  several 
cylinders.  In  order  to  illustrate  the  method  of  constructing  such  cards,  a  cross  com- 
pound engine  will  be  assumed. 

In  such  an  engine  steam  is  admitted  at  boiler  pressure  to  the  H.P.  cylinder  up  to 
the  point  of  cut-off.  After  the  H.P.  inlet  valve  is  closed,  the  steam  in  that  cylinder 
expands  until  the  end  of  the  stroke,  when  the  exhaust  valve  opens.  If,  as  is  usually 
the  case,  the  receiver  pressure  is  less  than  the  terminal  pressure  of  the  H.P.  cylinder, 
there  will  be  a  sudden  drop  in  pressure  in  the  H.P.  cylinder,  and  a  sudden  rise  in  the 
pressure  in  the  receiver,  at  the  instant  of  release.  The  H.P.  piston  will  now  begin 
to  return,  compressing  the  exhaust  steam  into  the  receiver  and  consequently  raising 
the  pressure,  both  in  the  receiver  and  in  the  H.P.  cylinder.  When  the  H.P.  piston 
reaches  mid-stroke,  the  L.P.  piston  arrives  at  the  end  of  its  stroke  and  the  L.P.  inlet 
valve  opens.  Unless  compression  is  complete  in  the  L.P.  cylinder,  steam  will  rush 
into  this  cylinder  from  the  receiver,  and  the  receiver  pressure  will  drop.  During  the 
remainder  of  the  back  stroke  of  the  H.P.  piston,  the  L.P.  piston  is  moving  forward, 
and  the  L.P.  cylinder  is  taking  steam  at  a  faster  rate  than  it  is  discharged  by  the  H.P. 
cylinder.  Since  the  steam  is  increasing  in  volume,  its  pressure  will  fall  until  the  L.P. 
inlet  valve  closes.  If  this  occurs  before  the  H.P.  exhaust  valve  closes,  the  pressure 
in  the  receiver  and  the  H.P.  cylinder  will  again  begin  to  rise.  If  it  occurs  after  the 
H.P.  exhaust  valve  closes,  the  pressure  in  the  receiver  will  not  rise  and  the  pressure 
in  the  H.P.  cylinder  will  rise  only  an  account  of  compression. 

Fig.  81  is  an  illustration  of  the  theoretical  card  given  by  such  an  engine;  a^b 
is  the  steam  line  of  the  H.P.  cylinder;  6-c  is  the  expansion  line  of  the  H.P.  cylinder; 
c-d  is  the  terminal  drop  of  this 
cylinder;  d-e  is  the  period  during 
which  the  H.P.  exhaust  is  being 
compressed  into  the  receiver  before 
the  L.P.  inlet  valve  opens;  e-f 
represents  the  drop  in  pressure  in 
the  H.P.  cylinder  when  the  L.P. 
inlet  valve  opens;  f-g  represents 
the  period  during  which  the  H.P. 
exhaust  and  the  L.P.  inlet  valves 
are  both  open ;  g-h  is  the  compres- 
sion period  in  the  H.P.  cylinder; 
f'-g'  is  the  admission  period  of  the 
L.P.  cylinder  up  to  the  time  when 

the  H.P.  exhaust  valve  closes;  g'-i'  is  the  remainder  of  the  admission  period,  which 
occurs  while  the  H.P.  exhaust  is  closed;  i'-j'  is  the  expansion  period  of  the  L.P. 
cylinder,  j'-k'  represents  the  L.P.  terminal  drop,  k'-l'  the  L.P.  exhaust;  l'-e'  repre- 
sents the  L.P.  compression  period,  and  e'-f  represents  the  rise  in  pressure  in  the 
L.P.  cylinder  at  the  point  of  admission  which  is  coincident  with  the  fall  in  pressure, 
p.-f,  in  the  H.P.  cylinder  and  the  receiver. 

In  computing  the  card  for  such  an  engine,  it  is  necessary  to  know  the  pressure  and 
volume  at  L.P.  release,  (/')>  and  the  initial  and  back  pressure  (i.e.,  at  ab,  and  k'-l'). 


FIG.  81. — Computed  card   for  a  cross  compound 
engine. 


168    NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES    ART.  192 

It  is  also  necessary  to  know  the  receiver  volume  (which  we  will  designate  by  the  symbol 
R)  and  the  volumes  of  the  high  and  low  pressure  cylinders  at  points  h,  b,  c,  e,  g,  ef,  g', 
i',  jf,  and  I'.  These  may  be  determined  graphically  when  the  clearance  volumes,  and 
the  points  of  cut  off  and  compression  are  known  for  each  cylinder.  In  order  to  illus- 
trate the  method  of  computing  the  card  the  following  example  will  be  assumed:  The 
initial  steam  pressure  is  150  pounds,  the  L.P.  terminal  pressure  10  pounds,  and  the 
back  pressure  2  pounds  per  square  inch  absolute.  The  swept  volume  of  the  H.P. 
cylinder  is  4  cubic  feet  and  of  the  L.P.  cylinder  15  cubic  feet.  The  H.P.  clearance 
volume  is  0.4  cubic  feet  (i.e.,  10  per  cent)  and  the  L.P.  clearance  volume  0.6  cubic  feet 
(i.e.,  4  per  cent).  The  receiver  volume  is  12  cubic  feet.  The  point  of  compression  is 
10  per  cent  from  the  end  of  the  stroke  for  each  cylinder,  and  L.P.  cut-off  occurs  at 
40  per  cent  of  the  stroke.  We  will  now  have 

F/-15.6  cu.ft. 
Vi'=   6.6     " 

ye'=  2.1    " 

Va-       -4      " 

y=  4.4    " 


In  order  to  find  the  volume  of  the  L.P.  cylinder  at  point  g',  we  may  make  the  con- 
struction shown  in  Fig.  82,  in  which  points  H  and    L  represent    the   simultaneous 

positions  of  the  H.P.  and  the  L.P.  cranks 
at  the  point  of  compression  in  the  H.P. 
cylinder,  distance  a  b  represents  the  distance 
of  the  point  of  compression  from  the  end  of 
the  stroke  of  the  H.P.  cylinder,  and  a  c  the 
distance  of  the  point  g'  from  the  end  of  the 
stroke  of  the  L.P.  cylinder.  From  such  a 
construction  we  find  the  distance  a  c  to  be 
20  per  cent  of  the  stroke,  and  the  volume 

Ty  =  3.6'cu.ft. 

The  product  of  the  pressure  and  volume  of 
the  steam  in  the  L.P.  cylinder  at  release  is 

Vj'  Pj'  =  15.6X10  =  156. 

The  product  of  the  pressure  and  volume  at 
cut-off  is  the  same,  and  the  pressure 


FIG.  82. 


The  pressure  in  the  receiver  at  this  point  is  the  same.  Consequently  the  product 
of  the  pressure  and  volume  of  the  steam  in  the  L.P.  cylinder  and  receiver  together 
at  this  point  is 

156  +  23.7X12=440. 


ART.  192     INDICATOR  CARDS  FOR  MULTIPLE  EXPANSION  ENGINES     169 

The  volume  of  the  steam  in  the  receiver  and  L.P.  cylinder  at  point  g'  is 

12  +  3.6  =  15.6cu.ft. 
The  pressure 


The  product  of  the  pressure  and  volume  of  the  steam  in  the  H.P.  cylinder,  the 
receiver,  and  the  L.P.  cylinder  at  the  instant  H.P.  Compression  begins  is  therefore 

440  +  28.2X0.8-462.6. 

The  volume  of  the  steam  contained  in  the  H.P.  cylinder,  the  receiver,  and  the  L.P. 
cylinder  at  L.P.  admission  is 

2.4  +  12  +  0.6  =  15cu.ft. 

We  will  therefore  have  for  the  pressure 

•     p/  '  =  P/  =  461-6  =  30.8  Ibs. 

The  product  of  the  pressure  and  volume  of  the  steam  contained  in  the  L.P.  cylin- 
der during  compression  is 

2X2.1=4.2. 

The  product  of  the  pressure  and  volume  of  the  steam  in  the  low  pressure  cylinder 
at  point  /'  is 

30.8X0.6  =  18.5. 

The  product  of  the  pressure  and  volume  of  the  steam  in  the  H.P.  cylinder  and  the 
receiver  at  point  e  is  therefore 

462.6-4.2=458.4. 
The  product  at  point  /  is 

462.6-18.5=444.1. 

Since  the  volume  of  the  steam  at  both  points  is   12+2.4  =  1.44  cu.ft.,  the  pressure 
at  e  is 


.. 
14.4 

The  volume  of  this  steam  at  d  is 

12+4.4  =  16.4  cu.ft., 
and  its  pressure  is 


The  pressure  of  the  steam  in  the  receiver  at  H.P.  release  is  P/  =  23.7,  and  the  product 
of  its  pressure  and  volume  is  therefore 

23.7X12=284. 

The  product  of  the  pressure  and  volume  of  the  steam  in  the  H.P.  cylinder  at  release 
is  therefore 

458.4-284  =  174.4. 

The  pressure  at  release  was  therefore 


~~  =39.7  Ibs. 
4.4 


170    NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES     ART.  103 
The  volume  at  H.P.  cut-off  was 

17/1/1 

1.162  cu.ft. 


and  cut-off  occurs  at  19  per  cent  of  the  stroke. 
The  pressure  at  e'  is 


the  pressure  at  h  is 


gXFg  _28.2X0.8  =  f) 


The  volume  of  the  cylinder  feed  is 

174.4-28.2X8 
150 


1.01  cu.ft. 


The  indicated  steam  consumption  per  stroke  is 

1.01X0.338  =  0.342  Ibs. 

The  actual  steam  consumption  per  stroke  may  be  estimated  by  adding  to  the  indicated 
steam  consumption  the  estimated  weight  of  the  steam  condensed  per  stroke,  and  an 
allowance  for  leakage.  The  power  of  the  engine  may  be  estimated  by  finding  the 
power  of  each  cylinder  shown  by  the  cards  obtained,  after  making  proper  reduction 
for  wire  drawing  and  steam  friction. 

'  193.  Combined  Cards  for  Multi-Cylinder  Engines.  The  combined 
card  of  a  steam  engine  is  obtained  by  placing  together  the  H.P.  card 
and  L.P.  card,  using  the  same  scale  of  pressures  and  the  same  scale  of 
volumes  and  setting  off  the  admission  line  of  the  two  cards  at  such 
distance  from  the  zero  volume  line  is  as  indicated  by  the  clearance  of  the 
respective  cylinders.  As  has  already  been  shown ,  when  the  same  weight 

of  cushion  steam  is  con- 
tained in  each  cylinder,  and 
the  compression  in  the  L.P. 
cylinder  is  complete  and 
there  is  no  compression  in 
the  H.P.  cylinder,  the  com- 
bined card  (except  for  over- 
lapping wire  drawing,  and 
H.P.  terminal  drop)  is  the 
same  as  would  be  given  in 
a  single  cylinder  engine 


FIG.  S3. — Theoretical  combined  cards.  having  the  volume    of    the 

L.P.  cylinder  and  the  same 

total  ratio  of  expansion.  If  the  same  weight  of  cushion  steam  is  con- 
tained in  each  cylinder,  but  the  conditions  of  compression  are  different, 
from  those  given,  the  card  will  be  that  which  would  be  given  by  a  cylinder 
of  different  swept  volume,  as  may  be  seen  in  Fig.  83,  in  which  the  length  A 


ART.  194  TESTING  STEAM  ENGINES  171 

represents  the  swept  volume  of  the  theoretical  cylinder  required  to  develop 
the  power  shown  by  the  card,  and  length  B  represents  the  swept  volume 
of  the  actual  low  pressure  cylinder.  The  swept  volume  plus  the  clear- 
ance volume  for  the  two  cylinders,  however,  will  be  the  same. 

When  the  weight  of  cushion  steam  contained  in  the  two  cylinders  is 
different,  it  will  be  impossible  to  draw  correctly  a  combined  card  which 
will  represent  the  action  of  the  steam,  since  the  weight  of  steam 
represented  by  the  H.P.  card  will  be  different  from  that  represented  by 
the  L.P.  card.  In  such  cases,  it  is  customary  to  refer  the  two  cards 
to  the  same  pressure  and  volume  scales.  The  theoretical  expansion 
line  for  the  two  cards  will  not,  however,  be  the  same. 

194.  Testing  Steam  Engines.     In  making  a  test  of  a  steam  engine 
it  is  usual  to  obtain  the  following  data: 

First,  the  pressure  of  the  steam  supplied  to  the  engine. 

Second,  the  quality  of  steam  supplied  to  the  engine. 

Third,  the  weight  of  wet  steam  rejected  by  the  engine. 

Fourth,  the  pressure  of  the  steam  in  the  condenser. 

Fifth,  the  temperature  of  the  water  entering  and  leaving  the  condenser. 

Sixth,  the  weight  of  the  drip  from  each  of  the  jackets. 

Seventh,  the  number  of  revolutions  per  minute  made  by  the  engine. 

Eighth,  indicator  cards  are  taken  from  each  end  of  each  cylinder. 

Ninth,  the  brake  horse-power  of  the  engine  is  obtained. 

The  precautions  which  must  be  observed  in  making  such  a  test  to 
insure  that  these  data  are  properly  taken  have  been  outlined  by  a  com- 
mittee of  the  American  Society  of  Mechanical  Engineers,  in  their  standard 
methods  of  testing  steam  engines.1  The  method  of  testing  here  outlined 
involves  the  use  of  a  surface  condenser.  When  any  other  type  of  con- 
denser is  employed,  the  weight  of  water  fed  to  the  boiler  and  not  the 
weight  of  steam  rejected  by  the  engine,  must  be  taken  as  the  measure 
of  the  steam  supplied.  An  engine  test  should  last  several  hours  and  the 
conditions  of  load,  steam  pressure,  vacuum,  etc.,  should  be  kept  as  nearly 
constant  as  possible.  Any  considerable  variation  in  these  quantities 
during  the  test  will  invalidate  the  results.  The  readings  are  taken  at 
frequent  intervals,  usually  every  ten  minutes. 

195.  Graphical  Analysis  of  an  Engine   Test.      It  is  instructive  in   working 
up  the  results  of  an  engine  test  to  superimpose  the  indicator  cards    of    the    engine 
upon  the  theoretical  diagram   of  the  cycle  in  order  to  determine  the  magnitude 
and  distribution  of  the  losses  which  occur.     In  order  to  do  this,  it  is  necessary  to 
construct  a  mean  card  for  each  of  the  cylinders,  which  will  represent  the  average  con- 
ditions for  both  the  head  and  crank  ends  of  that  cylinder  for  the  entire  test. 

After  computing  the  average  mean  effective  pressure  developed  during  the  entire 

1  See  the  Transactions  of  the  A.S.M.E.  for  1902.  The  rules  are  also  published  by 
the  Society  in  pamphlet  form. 


172    NOTES  ON   DESIGN  AND  TESTING  OF  STEAM  ENGINES    ART.  195 

test  in  the  head  and  crank  end  of  each  cylinder,  that  set  of  indicator  cards  is  chosen 
in  which  the  mean  effective  pressures  are  nearest  to  the  average.  These  cards  are, 
f  course,  the  best  representative  cards  for  the  test.  Each  of  the  cards  may  then  be 
ruled  with  a  number  of  equidistant  vertical  lines,  as  shown  in  Fig.  84.  Upon  the 
paper  on  which  the  mean  card  is  to  be  constructed  for  any  cylinder,  rule  a  horizontal 
line,  for  the  atmospheric  line,  making  its  length  represent  the  swept  volume  of  both 
ends  of  the  cylinder,  to  any  suitable  scale.  Upon  it  erect  the  same  number  of  equi- 
distant vertical  lines  as  has  already  been  drawn  upon  each  of  the  indicator  cards. 


Head  End  Card 


Crank  End  Card 


\ 


\ 


\ 


\ 


\l 


a'  Mean  Card 

FIG.  84. — Construction  of  a  mean  card. 

Upon  the  first  vertical  line  of  the  head  end  card,  measure  the  distance  from  the 
atmospheric  line  to  a  point  on  the  outline  of  the  card,  as  a-b.  Add  to  this  distance 
the  corresponding  distance  c-d  measured  upon  the  crank  end  card,  and  lay  off  upon 
the  first  vertical  line  of  the  mean  card  the  sum  of  the  distances  a-b  and  c-d,  at  a'd'. 
In  like  manner  lay  off  all  the  other  points  and  so  draw  a  card  which  is  the  mean  of  the 
head  and  crank  end  cards  for  the  cylinder.  The  zero  pressure  line  may  now  be  drawn 
parallel  with  the  atmospheric  line,  the  distance  between  the  lines  being  determined 
by  the  atmospheric  pressure  at  the  time  of  the  test,  as  computed  from  the  barometer 
reading.  The  zero  volume  line  is  drawn  perpendicularly  to  the  atmospheric  line  at 
such  a  distance  from  the  end  of  the  mean  card  as  represents  the  sum  of  vhe  head  and 


ART.  195 


GRAPHICAL   ANALYSIS  OF  AN  ENGINE  TEST 


173 


crank  end  clearance  volumes.  The  theoretical  indicator  card  for  a  Rankine  cycle 
with  complete  compression  is  now  constructed,  the  weight  of  cushion  steam  and  the 
weight  of  working  fluid  being  the  same  for  the  Rankine  cycle  as  it  is  for  the  cylinder 
in  question.  The  quality  of  the  steam  at  cut-off  and  at  the  beginning  of  compression, 
in  the  Rankine  cycle,  is  assumed  to  be  the  same  as  that  of  the  cylinder  feed,  as  deter- 
mined during  the  engine  test.  The  pressure  limits  of  the  Rankine  cycle  are,  in  the  case 
of  the  H.P.  cylinder  of  a  multiple  expansion  engine,  the  pressure  of  the  steam  at  the 
throttle  valve  and  that  of  the  steam  in  the  receiver.  In  the  case  of  an  intermediate 
cylinder,  the  pressure  limits  of  the  Rankine  cycle  are  the  pressures  of  the  steam  in  the 
preceding  and  following  receivers.  In  the  case  of  the  L.P.  cylinder  of  a  multiple  expan- 
sion engine,  they  are  the  pressure  of  the  steam  in  the  preceding  receiver  and  the  pres- 


f  N 

FIG.  85. — Actual  card  superimposed  upon  a  Rankine  cycle  card  to  show  the  losses. 

sure  corresponding  to  the  temperature  of  the  discharged  condensing  water.  In  the 
case  of  a  simple  non-condensing  engine,  the  pressure  limits  are  the  pressure  of  the 
steam  at  the  throttle  and  the  pressure  of  the  atmosphere. 

Fig.  85  shows  the  construction  for  the  L.P.  cylinder  of  a  compound  engine,  the 
heavy  outline  being  the  actual  indicator  card,  while  the  light  outline  is  the  theoretical 
card  for  the  Rankine  cycle.  Since  terminal  drop  is  employed,  the  toe  of  the  Rankine 
cycle,  bounded  by  the  lines  cdN,  will  be  lost.  This  loss  is  due  to  the  imperfection  of 
the  cycle  employed.  A  line  g-h  drawn  parallel  with  the  line  f-d  (which  represents 
the  pressure  corresponding  to  the  temperature  of  the  discharged  condensing  water) 
and  tangent  to  the  actual  card,  marks  off  the  area  ghfN  is  which  represents 
the  loss  due  to  the  imperfection  of  the  condensing  apparatus.  The  expansion  line 


FIG.  86. — Card  from  a  non-condensing  engine  superimposed  on  a  Rankine  cycle  card. 

of  the  steam  may  now  be  completed,  and  is  represented  by  the  line  je.  The  area 
j-b-c-e  will  then  represent  the  loss  of  power  due  to  cylinder  condensation.  The  shaded 
area  minus  the  dotted  area  represents  the  loss  of  power  due  to  the  combined  effects 
of  steam  friction,  wire  drawing,  and  overlapping.  The  smaller  the  volume  of  the  receiver, 
the  larger  will  be  the  amount  of  this  loss.  The  area  a-K-L  represents  the  loss  due  to 
clearance.  There  is  a  further  loss  due  to  clearance  included  in  the  area  c-d-f  on 
account  of  the  incomplete  expansion  of  the  steam  compressed  in  the  clearance  spaces. 
If  an  adiabatic  expansion  line  j-i  be  constructed  from  point  /,  the  area  e-j-i  will  be  the 
work  restored  by  the  re-evaporation  of  the  steam  initially  condensed.  A  part  of  this 
work  so  restored  is,  of  course,  lost  from  other  causes.  The  area  in  the  lower  left- 


174     NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES    ART.  196 

hand  corner,  bounded  by  the  compression  line  and  by  the  line  L-h,  is  the  work  lost 
on  account  of  the  compression  of  dry  and  saturated  steam  which  results  from  the  heat- 
ing of  the  exhaust  by  the  cylinder  walls. 

Fig.  86  represents  a  card  similarly  treated  for  a  simple  non-condensing  engine. 
The  losses  may  be  traced  out  by  the  reader. 

196.  Other  Methods   of    Analyzing    Engine    Tests.     A    method    formerly 
much  in  use  in  analyzing  the  results  of  an  engine  test  is  that  known  as  Hirn's  analysis. 
In  this  method,  the  heat  transferred  to  or  from  the  steam  contained  in  the  cylinder  is 
determined  for  each  portion  of  the  cycle.     It  is  assumed  in  Hirn's  analysis  that  all 
heat   transfers  not   otherwise  accounted  for  are  due  to  cylinder  condensation  or  re- 
evaporation.     This  is  not  true,  since  such  heat  transfers  are  often  due  to  leakage. 
The  computations  involved  in  Hirn's  analysis  are  rather  laborious,  as  may  be  seen  by 
reference  to  Art.  55  of  the  second  volume  of    Zeuner's  Technical  Thermodynamics, 
in  which  the  theory  of  Hirn's  analysis  is  fully  developed.     Hirn's  method  of  analysis 
emphasizes  unduly  the  losses  due  to  cylinder  condensation,  and  does  not  separate  or 
analyze  other  sources   of  loss.     On  this  account,  Hirn's  method  of  analysis  is  not 
much  used  at  the  present  time  in  determining  the  amount  and  distribution  of  the 
losses  in  the  steam  engine. 

Another  method  of  determining  the  losses  in  a  steam  engine  is  to  draw  the  tem- 
perature-entropy diagram  of  the  fluid  contained  in  the  cylinder  and  then  to  superimpose 
this  diagram  upon  the  theoretical  temperature-entropy  diagram  of  the  cycle  in 
the  manner  shown  in  Chapter  XXV.  The  temperature-entropy  diagram  has 
the  advantage  of  illustrating  more  clearly  the  heat  transfer  to  and  from  the 
cylinder  walls,  but  it  is  more  difficult  to  employ  than  the  methods  described  in  Art. 
195,  which  are,  on  the  whole,  the  most  satisfactory  methods  of  analyzing  the  results 
of  an  engine  test. 

197.  Methods    of    Comparing    Engine    Efficiencies.     Many  methods 
are  in  use  for  stating  the  efficiencies  of  steam  engines.     One  of  the  com- 
monest is  to  determine  the  number  of  pounds  of  dry  steam  supplied  per 
hour  to  the  engine  per  indicated  horse-power  developed.     This  is  usually 
known  as  the  water  rate  of  the  engine.     While,  in  general,  a  low  water 
rate  means  a  highly  efficient  engine,  the  water  rates  of  different  types  of 
engines   are   not   proportional   to   their   true   economy.     Accordingly,    a 
second  method  has  been  suggested  in  which  the  efficiency  of  the  engine  is 
expressed  in  terms  of  its  heat  rate  (i.e.,  in  terms  of  the  number  of  B.T.U. 
supplied  to  the  engine  per  indicated  horse-power  per  hour).     The  heat 
rate  may  be  derived  from  the  water  rate  by  subtracting  from  the  total 
heat  of  the  dry  steam  supplied,  the  heat  of  the  liquid  at  the  temperature 
of  exhaust,  and  multiplying  by  the  water  rate.     Sometimes  the  number 
of  B.T.U.  supplied  per  brake  horse-power  is  given.     In  the  case  of  direct 
connected  units,  the  efficiency  of  the  combined  unit  is  often  expressed 
by  the  number  of  B.T.U.  supplied  per  kilowatt  hour  output  of  the  gen- 
erator.    Occasionally   the   number   of   B.T.U.   per   minute  is   made   the 
basis  of  the  statement  of  efficiency.     The  efficiency  is  often  expressed  as 
a  per  cent  of  the  theoretical  efficiency  of  the  Rankine  cycle.      The  effi- 
ciency referred  to  the  Rankine  cycle  may  be  obtained  by  dividing  the 


ART.  198          RELATION  BETWEEN  LOAD  AND  EFFICIENCY 


175 


heat  rate  of  the  Rankine  cycle  for  the  given  temperature  range  by  the 
heat  rate  of  the  actual  engine  for  the  same  temperature  range.  The 
total  efficiency  of  an  engine  is  sometimes  given ;  which  is  the  per  cent 
of  the  total  heat  supplied  which  is  actually  transformed  into  useful  work. 
In  the  table  given  in  Art.  210,  will  be  found  recent  figures  for  the  best 
efficiencies  of  steam  engines  and  turbines,  in  which  the  efficiencies  are 
stated  in  the  different  ways  most  commonly  employed. 

198.  Effect  of  Variation  in  the  Load  on  the  Efficiency.  The  power 
developed  by  an  engine  is  not  a  fixed  quantity,  but  is  usually  automatically 
varied  by  the  governor  in  such  a  manner  as  to  keep  the  speed  of  the  engine 


.Hi 


10 


IbO 


200 


60  80  100  130  140 

Load  in  per  cent  of  the  Bated  Load . 

FIG.  87. — Load  curve  of  a  steam  engine. 

constant.  The  governor  accomplishes  this  by  increasing  or  diminishing 
the  quantity  of  steam  per  stroke  taken  by  the  engine.  As  a  result  of  the 
action  of  the  governor,  the  form  of  the  steam  cycle  and  the  conditions 
of  operation  vary  as  the  load  on  the  engine  is  varied.  In  consequence 
of  these  changes  the  losses  vary,  being  usually  less  at  low  loads  than  at 
high  loads.  If  the  sum  of  the  losses  were  always  proportional  to  the 
power  developed,  the  efficiency  of  the  engine  would  be  constant  at 
all  loads.  Since  such  is  not  the  case,  it  follows  that  at  some  particular 
load  the  heat  rate  of  the  engine  will  be  a  minimum  (i.e.,  its  efficiency 
will  be  a  maximum)  and  at  all  other  loads  the  heat  rate  will  be  increased. 
The  rated  power  (i.e.  the  nominal  horse-power)  of  a  steam  engine  is 
usually  the  indicated  horse-power  at  which  it  gives  the  minimum  heat 


176     NOTES  ON  DESIGN  AND  TESTING  OF  STEAM  ENGINES     ART.  198 


consumption  per  brake  horse-power  per  hour.  In  the  case  of  other  types  of 
heat  engines  (e.g.,  steam  turbines  and  gas  engines)  this  is  not  true,  since 
such  engines  give  the  greatest  economy  at  the  maximum  possible  load, 
and  if  rated  at  their  most  economical  load  they  would  have  no  overload 
capacity.  The  efficiency  of  a  steam  engine  falls  off  rapidly  at  low  loads, 
as  may  be  seen  by  referring  to  the  "  load  curve  "  shown  in  Fig.  87,  and 
it  is  therefore  desirable  to  operate  such  an  engine  at  or  above  its  rated 
load.  Consequently  when  a  plant  is  to  furnish  a  variable  amount  of 
power,  several  engines  should  be  installed,  and  such  a  number  of  them 
should  be  operated  at  any  time  as  will  make  the  load  on  each  one  as 
nearly  as  possible  equal  to  its  rated  load. 

Furthermore,  in  comparing  the  efficiency  of  different  engines,  it  is 
necessary  to  compare  their  efficiencies  at  their  most  economical  loads, 
since  comparison  on  any  other  basis  would  be  misleading.  A  statement 
of  the  results  of  an  engine  test  should  therefore  always  include  a  state- 
ment of  the  actual  and  of  the  rated  load  of  the  engine,  in  order  that  it 
may  be  known  whether  the  conditions  of  operation  were  such  as  to  make 
reasonable  economy  possible. 

In  the  case  of  an  engine  with  a  throttling  governor,  the  total  steam 

consumption   of   the    engine 
is   given  approximately    by 


y 


the  formula 


O        A  20          40  60  80  100         120        HO 

Indicated  Horse  Power  in  Terms  of  the  Rated  Load 

FIG.  88. — Curve  of  total  steam  consumptign. 


in  which  S  is  the  total  steam 
consumption,  A  and  K  are 
constants,  and  H.P.  is  the 
brake  horse-power  developed 
by  the  engine.  This  is  known 
as  Willan's  Law.  It  does 
not  hold  for  cut-off  governed 
engines,  for  which  we  may 
write  an  approximate 
mula  of  the  form 


for- 


in  which  n  is  greater  than  one.  The  general  form  of  the  curve  of  total 
steam  consumption  for  such  an  engine  is  shown  in  Fig.  88.  In  this  figure 
the  segment  0  A  is  equal  to  the  friction  horse-power.  A  line  through  0 
tangent  to  the  curve  of  total  steam  consumption  will  obviously  touch  it 
at  the  point  where  the  water  rate  per  indicated  horse-power  is  a  minimum. 
In  like  manner,  a  tangent  through  A  will  touch  it  at  the  point  where  the 
water  rate  per  brake  horse-power  is  a  minimum. 


ART  198  PROBLEMS  177 

A  flat  load  curve  is  a  desirable  characteristic  in  an  engine,  and  when 
two  engines  of  equal  efficiency  are  compared,  that  one  is  the  better  which 
has  the  flatter  load  curve. 

PROBLEMS 

1.  A  steam  turbine  plant  costs  $60.00  per  kilowatt,  while  a  steam  engine  plant 
costs  $80.00  per  kilowatt.     If  the  fixed  charges  are   15  per  cent  per  annum  in  each 
case,  and  the  plant  operates  15  hours  per  day,  for  300  days  per  year,  what  will  be  the 
costs  per  kilowatt  hour  due  to  fixed  charges  on  the  plant? 

Ans.     0.200  cents  and  0.267  cents. 

2.  The  steam  turbine  plant  requires  2  Ibs.  of  coal  per  kilowatt  hour,  and  the  steam 
engine  plant  1.8  Ibs.  per  kilowatt  hour.     Coal  costs  $2.00  per  ton.     What  is  the  cost 
per  kilowatt  hour  in  each  case?  Ans.     0.10  cents  and  0.09  cents. 

3.  Which  of  the  two  plants  will  operate  at  the  least  total  cost  per  kilowatt  hour, 
disregarding  all  other  costs  except  those  given? 

Ans.     The  turbine  plant  will  operate  at  0.300  cents  and  the  engine  plant  at 
0.357  cents  per  kilowatt  hour. 

4.  Construct  a  combined  card  for  a  compound  engine  taking  steam  at  150  Ibs. 
gage  and  discharging  it  at  2  Ibs.  absolute.     The  clearance  of  the  low  pressure  cylinder 
is  5  per  cent  and  the  pressure  at  the  end  of  compression  0  Ibs.  absolute.     The  ratio 
of  expansion  is  16-     Assume  hyperbolic  expansion  and  compression. 

5.  Divide  the  above  card  into  two  parts  so  that  the  areas  of  the  two  parts  are  equal. 

6.  Give  sufficient  terminal  drop  to  the  H.P.  card  so  that  the  total  steam  load  on 
the  H.P.  piston  will  be  equal  to  that  on  L.P.  piston,  at  the  instant  when  the  load  is  a 
maximum  in  each  cylinder.     (The  total  steam  load  is  equal  to  the  area  of  the  piston 
times  the   difference   in   steam   pressure   at   inlet   and   exhaust.)     Assume  that   the 
lengths  of  stroke  are  equal  for  the  two  cylinders  and  that  the  areas  of  the  cylinders 
are  proportional  to  the  volumes. 

7.  Find  the  mean  effective  pressure  of  the  above  card  referred  to  the  L.P.  cylinder, 
assuming  a  card  factor  of  90  per  cent. 

8.  What  must  be  the  diameter  of  the  L.P.  cylinder  of  an  engine,  in  order  that  it 
shall  develop  500  indicated  horse-power  at  600  ft.  per  minute  piston'  speed,  with  the 
M.E.P.  found  in  Problem  7. 

9.  Find  the  proper  volume  for  the  receiver  for  the  above  engine,  assuming  that  it 
is  to  be  a  cross  compound  engine. 

10.  An  engine  uses  10,000  Ibs.  of  steam  of  98  per  cent  quality  in  a  2-hour  test. 
The  indicated  horse-power  is  250.     What  is  the  water  rate  of  the  engine? 

Ans.     19.6  Ibs.  per  hour. 

11.  If  the  steam  is  supplied  at   125  Ibs.  gage  pressure  and  the  condenser  pressure 
is  3  Ibs.  absolute,  what  is  the  heat  rate  of  the  above  engine?        Ans.     21,310  B.T.U. 

12.  If  the  mechanical  efficiency  of  the  engine  is  92  per  cent,  what  is  the  heat  rate 
per  brake  horse-power  per  hour?  Ans.     22070  B.T.U. 

13.  What  is  the  heat  rate  of  the  Rankine  cycle  for  the  same  temperature  range? 

Ans.     10,810  B.T.U. 

14.  What  is  the  brake  efficiency  of  the  above  engine  expressed  as  a  percent  of  the 
efficiency  of  the  Rankine  cycle?  Ans.     49% 

15.  What  is  the  total  efficiency  of  tluj  above  engine?  Ans.     11.5% 


CHAPTER   XII 


THE    STEAM    TURBINE 

199.  Impulse  and  Reaction  Turbines.     The  steam  turbine  is  a  heat 
engine  which  makes  use  either  of  the  impulse  or  of  the  reaction  of  a  jet 
of  steam,  in  order  to  transform  the  energy  of  this  steam  into  work.     If 
the  turbine  operates  by  utilizing  the  impact  of  the  steam  jet,  it  is  known 
as  an  impulse  turbine.     If  it  makes  use  of  the  reaction  of  the  steam  jet, 
it  is  known  as  a  reaction  turbine.      Turbines  which  combine  both  prin- 
ciples are  sometimes  used  and  are  known  as  impulse-reaction  turbines. 
The  impulse  turbine  is  sometimes  termed  the  velocity  turbine,  and  the 
reaction  turbine  is  sometimes  termed  the  pressure  turbine. 

200.  The   Theory   of   the   Turbine   Nozzle.       If   steam   be    supplied 
under  pressure  to  a  properly  shaped  nozzle,  it  will  flow  from  the  nozzle 

with  a  very  high  velocity  in  the 
form  of  a  jet.  If  this  jet  be 
permitted  to  strike  upon  a  suit- 
ably formed  surface  so  that  its 
direction  of  motion  is  changed, 
as  in  Fig.  89,  the  impact  of  the 
jet  upon  the  surface  will  tend  to 
force  the  surface  backwards,  and 
if  the  surface  be  permitted  to 
move,  work  will  be  performed. 
The  Kerr  turbine,  illustrated,  in 
Fig.  90,  is  of  this  type.  If  the 
nozzle  itself  be  permitted  to 
move,  the  reaction  of  the  escap- 
ing steam  will  force  it  backward, 
and  work  will  be  performed.  This 
is  the  principle  of  the  reaction 
turbine.  The  Avery  turbine, 

illustrated  in  Fig.  91,  is  of  this  type.  It  will  be  seen  that  the  proper 
operation  of  a  steam  turbine  will  depend  upon  the  form  of  the  nozzles 
used.  It  is  therefore  a  matter  of  primary  importance  in  steam  turbine 
design  to  make  the  nozzles  of  the  proper  form  and  size  for  the  work 
which  they  are  to  do.  The  following  paragraphs  will  serve  to  make 

178 


FIG.  89. — Impact  of  steam  jet  upon  a 
properly  formed  vane  surface. 


ART.  200 


THE  THEORY  OF  THE  TURBINE  NOZZLE 


170 


clear    the    action    of    turbine    nozzles    and    the    methods    of    designing 
them. 

When  steam  flows  through  a  nozzle  each  particle  will  be  found  to 
expand  in  volume  and  increase  in  velocity  as  it  passes  from  the  region 
of  high  pressure  to  that  of  low  pressure.  In  passing  through  the  nozzle, 
the  steam  will  neither  gain  nor  lose  heat.  This  being  the  case,  the  kinetic 
energy  of  each  pound  of  steam  as  it  passes  a  given  cross-section  of  the 
nozzle,  plus  the  work  done  by  this  steam  in  displacing  the  steam  in  the 
region  into  which  it  rushes,  must  be  equal  to  the  loss  of  internal  energy 
of  this  pound  of  steam,  plus  the  work  done  upon  it  by  the  advancing 


FIG.  90. — Section  of  a  Kerr  turbine. 

mass  of  steam  which  takes  its  place  in  the  region  from  which  it  flows. 
A  consideration  of  Fig.  92  will  make  this  apparent. 

In  the  figure  A  is  a  cylinder  and  B  a  nozzle.  The  cross-section  of 
the  nozzle  is  very  small  in  comparison  with  that  of  the  cylinder,  so  that 
the  velocity  of  the  steam  in  the  cylinder  may  be  neglected.  The  steam 
flowing  from  the  nozzle  passes  into  the  tube  (7,  whose  cross-section  is 
the  same  as  that  of  the  nozzle  at  the  point  where  the  nozzle  terminates. 
Assume  that  cylinder  A  is  filled  to  the  point  d  with  a  steam  having  a 
pressure  PI  and  entropy  N,  and  that  tube  C  is  filled  to  the  point  E 
with  steam  having  a  pressure  P2.  Since  the  steam  neither  gains  nor 
loses  heat  in  passing  through  a  frictionless  nozzle,  the  entropy  in  tube  C 
will  be  the  same  as  in  cylinder  A,  and  the  expansion  is  adiabatic.  At 
E  in  the  tube  and  at  D  in  the  cylinder  are  pistons  which'  exert  upon  the 


180 


THE  STEAM  TURBINE 


ART.  200 


steam  a  pressure  equal  to  that  exerted  upon  them  by  the  steam.     The 

pressure  in  tube  C  being  less  than  that  in  cylinder  A,  the  steam  will  flow 
from  AtoC  through  the  nozzle,  and  if  the  pres- 
sures are  to  remain  constant,  the  pistons  must 
both  move  to  the  right.  Assume  that  the  pro- 
portions of  the  nozzle  are  such  that  1  pound 
of  steam  flows  per  second,  then  the  work  done 
upon  the  steam  per  second  by  piston  D  will  be 
the  external  work  of  evaporation  of  1  pound  of 
steam  of  pressure  PI  and  entropy  N.  The  work 
done  by  the  steam  upon  piston  E  will  be  equal 
to  the  external  work  of  evaporation  of  1  pound 
of  steam  at  pressure  P^  and  of  entropy  N. 
The  kinetic  energy  of  the  pound  of  steam  flow- 
ing in  the  tube  C  will  then  be  equal  to  the 
work  of  expansion  (which  is  the  difference 
between  the  internal  energy  of  a  pound  of 
steam  when  in  cylinder  A  and  in  the  tube  C) 
plus  the  work  done  by  piston  Z),  minus  the 
work  done  upon  piston  E.  This  is  of  course 
equal  to  the  difference  between  the  total  heat 
of  the  pound  of  steam  at  pressure  PI  and  entropy 
Nj  and  its  total  heat  at  the  same  entropy  and 
at  the  pressure  P2,  a  quantity  which  we  will 
designate  by  the  symbol  AH,  and  which  is 

usually  termed   the  heat  drop.      The   kinetic   energy   of   a   body   having 

a  mass  of  1  pound  is  of  course 


FIG.  91. — Diagram  illus- 
trating the  principle  of 
the  A  very  turbine. 


e        C 


FIG.  92. — Ideal  apparatus  illustrating  the  flow  of  steam  through  a  nozzle, 
We  have  already  seen  that 


whence 


72 
64.34 


777.5  JH. 


(2) 
(3) 


ART.  201  FORM  OF  THE  TURBINE  NOZZLE  181 

Solving  for  V,  the  velocity  of  the  steam  leaving  the  nozzle, 


7=^61.34X777.8  AH  =  223.6 V/IH.   ...     (4) 

201.  Form  of  the  Turbine  Nozzle.  As  the  steam  flows  through  the 
nozzle  H  increases  in  velocity  and  volume  and  diminishes  in  pressure. 
The  area  at  any  section  is  directly  proportional  to  the  specific  volume  of 
the  steam  and  inversely  proportional  to  its  velocity.  If  the  cross-sec- 
tional areas  at  a  series  of  points  in  the  nozzle  be  computed  it  will  be 
found  that  the  areas  diminish  at  first  until  the  pressure  in  the  nozzle 
becomes  about  58  per  cent  of  the  initial  absolute  pressure  of  the  steam, 
and  from  that  point  onward  the  areas  again  begin  to  increase.  The  point 
of  minimum  section  is  known  as  the  throat  of  the  nozzle.  The  quantity 
of  steam  discharged  by  the  nozzle  obviously  depends  on  the  area  of  the 
throat  or  minimum  section  provided  the  steam  is  discharged  into  a  region 
in  which  the  pressure  is  less  than  58  per  cent  of  the  initial  steam  pressure. 

In  order  to  have  a  nozzle  discharge  steam  with  a  minimum  of  tur- 
bulence and  friction,  it  is  advisable  that  the  acceleration  of  the  body 
of  steam  contained  within  it  shall  be  constant.  Such  a  constant  accelera- 
tion requires  of  course  that  the  amount  of  heat  energy  transformed  into 
work  between  any  two  cross-sections  shall  be  proportional  to  the  dis- 
tance between  these  sections.  A  nozzle  of  the  proper  form  may  therefore 
be  computed  in  the  following  manner: 

First,  having  given  the  initial  pressure  and  quality  of  the  steam,  its 
entropy  should  be  found.  Second,  choose  a  series  of  pressures  whose 
saturation  temperatures  differ  by  an  approximately  constant  amount. 
Third,  from  the  known  entropy  of  steam  during  its  adiabatic  expansion, 
compute  the  total  heat  and  specific  volume  of  the  steam  at  these  several 
pressures.  Fourth,  compute  the  heat  drop  (i.e.,  the  quantity  JH)  for 
each  of  the  several  pressures.  Fifth,  compute  the  resulting  velocity  at 
each  of  the  several  pressures.  Sixth,  from  the  velocity  and  specific 
volume  of  the  steam  at  each  of  the  several  pressures,  determine  the 
proper  cross-sectional  area  of  the  nozzle.  Seventh,  compute  the  diameter 
of  the  section  for  each  of  these  several  areas.  Eighth,  make  the  distance 
of  each  section  from  the  inlet  end  of  the  nozzle  proportional  to  the  heat 
drop.  These  computations  may  be  made  from  Marks  and  Davis's  Steam 
Tables  or  may  be  approximately  determined  from  the  total  heat  entropy 
diagram.  It  is  usually  more  convenient,  however,  to  make  them  by 
means  of  Peabody's  temperature-entropy  table.  The  method  of  per- 
forming the  computations  may  be  seen  from  the  following  example. 

Required  to  design  a  turbine  nozzle  to  discharge  10,000  pounds  of 
steam  per  hour,  the  initial  pressure  of  the  steam  being  175  pounds  absolute 
and  the  initial  superheat  96°.  The  nozzle  discharges  into  a  pressure 


182 


THE  STEAM  TURBINE 


AttT.  201 


of  20  pounds  absolute.  Assume  that  the  entering  velocity  of  the  steam 
at  the  mouth  of  the  nozzle  is  100  feet  per  second.  From  Peabody's 
temperature -entropy  table,  the  nearest  pressure  is  175.3  pounds  and  the 
nearest  superheat  is  95°. 7.  The  entropy  is  1,62.  The  work  can  be  most 
easily  performed  by  tabulating  it  in  the  manner  shown  in  Table  X. 

TABLE  X 


p 

H 

AH 

U 

Vel. 

Sp.  V. 

A, 

A 

D 

L 

175.3 

1251.2 

0.2 

100 

3.018 

0.03018 

12.07 

3.93 

0.0 

169.0 

1247.6 

3.6 

3.8 

435 

3.102 

0.00714 

2.856 

1.91 

0.126 

162.8 

1244.0 

7.2 

7.4 

608 

3.190 

0.00525 

2.100 

1.64 

0.259 

156.8 

1241.4 

10.8 

11.0 

741 

3.280 

0.00442 

1.768 

1.501 

0.378 

152.9 

1238.0 

13.2 

13.4 

818 

3.343 

0.00409 

1.636 

1.443 

0.469 

134  .  5 

1226.3 

24.9 

25.1 

1120 

3.605 

0.00329 

1.316 

1.296 

0.872 

117.9 

1214.7 

36.5 

36.7 

1354 

4.079 

0.00301 

1.204 

1.340 

1.278 

101.6 

1201.8 

49.4 

49.6 

1574 

4.566 

0.00290 

1.160 

1.217 

1.730 

89.6 

1191.2 

60.0 

60.2 

1735 

5.018 

0.00290 

1.160 

1.217 

2.10 

77.6 

1179.4 

71.8 

72.0 

1896 

5.610 

0.00296 

1.184 

1.230 

2.52 

67.0 

1167.7 

83.5 

83.7 

2042 

6.384 

0.00312 

1.248 

1.251 

2  92 

57.5 

1155.9 

95.3 

95.5 

2183 

7.290 

0.00334 

1.336 

1.304 

3.34 

49.19 

1143.9 

107.3 

107.5 

2316 

8.368 

0.00362 

1.448 

1.360 

3.76 

41.84 

1131.6 

120.6 

120.8 

2458 

9.639 

0.00392 

1.568 

1.415 

4.22 

35.32 

1119.4 

131.8 

132.0 

2567 

11.16 

0.00435 

1.740 

1.490 

4.61 

29.82 

1106.9 

144.3 

144.5 

2687 

12.99 

0.00482 

1.928 

1.570 

5.05 

24.97 

1094.3 

156.9 

157.1 

2800 

15.18 

0.00543 

2.172 

1.665 

5.49 

20.02 

1079.0 

172.2 

172.4 

2935 

18.46 

0.00629 

2.516 

1.792 

6.02 

In  the  first  column,  headed  P,  will  be  found  the  successive  pressures 
for  which  the  dimensions  of  the  nozzle  are  to  be  computed.  In  the  column 
headed  H  will  be  found  the  total  heat  of  the  steam  at  the  given  pressure, 
and  entropy  1.62,  as  obtained  from  the  temperature-entropy  table.  In 
the  column  headed  AH  will  be  found  the  difference  between  the  initial 
total  heat  and  the  total  heat  at  the  pressure  given.  In  the  column 
headed  U  will  be  found  the  heat  drop  plus  the  initial  kinetic  energy  of 
the  steam  in  B.T.U.  In  the  column  headed  Vel.  will  be  found  the  velocity 
of  the  steam.  In  the  column  headed  Sp.V.  will  be  found  the  specific 
volume  of  the  steam  as  taken  from  the  steam  tables.  In  the  column 
headed  AI  will  be  found  the  area  of  a  nozzle  in  square  feet,  per  pound 
of  steam  flowing  per  second.  In  the  column  headed  A  will  be  found  the 
actual  area  of  the  nozzle  in  square  inches  to  pass  10,000  pounds  of  steam 
per  hour.  In  the  column  headed  D  will  be  found  the  diameter  of  the 
nozzle  in  inches,  and  in  the  column  headed  L,  the  length  in  inches  from 
the  inlet  end  of  the  nozzle  to  the  section  having  the  diameter  given. 
The  following  formulae  will  be  used  in  making  the  various  computa- 
tions : 


ART.  202 


FORM  OF  THE  TURBINE  NOZZLE 


183 


Vel.  =  223.6V7  'U, 

Sp.V. 
1      VeL  ' 


10000 
3600 ' 


L  =  K  AH, 

in  which  K  is  a  constant  so  chosen  as  to  make  the  nozzle  of  reasonable 
length.     The  form  of  the  nozzle  so  computed  is  illustrated  in  Fig  93. 


FIG.  93. — Form  of  turbine  nozzle  giving  constant  steam  acceleration. 

202.  Alternate  Methods  of  Designing  a  Turbine  Nozzle.  It  will  be 
seen  that  the  work  of  computing  the  exact  form  of  a  nozzle  which  will 
give  constant  acceleration  to  the  steam  becomes  laborious  when  a  tem- 
perature-entropy table  is  not  available.  Consequently,  steam  turbine 
nozzles  are  usually  designed  by  finding  the  area  of  the  throat  and  of  the 
mouth  of  the  nozzle  and  making  the  nozzle  of  the  form  shown  in  Fig. 
94.  The  radius  of  the  entering  portion  should  be  made  equal  to  the 
diameter  of  the  throat  in  case  a  circular  nozzle  is  employed.  The 
divergent  portion  of  the  nozzle  is  a  frustrum  of  a  cone,  the  elements  of 
which  make  an  angle  of  about  5°  with  the  axis.  Sometimes  the  throat 
is  made  straight  for  a  distance  equal  to  one-half  its  diameter  as  shown 


184 


THE  STEAM  TURBINE 


ART.  202 


in  Fig.  95.  Either  of  these  forms  gives  a  nozzle  of  high  efficiency,  although 
it  is  not  reasonable  to  suppose  that  the  efficiency  would  be  as  high  as  in 
the  case  of  a  nozzle  designed  to  give  constant  acceleration  to  the  steam. 
The  work  of  designing  a  nozzle  like  that  in  Fig.  94  may  be  seen  from  the 


FIG.  94. — Turbine  nozzle  of  the  usual  form. 

following  example,  in  which  quantities  from  Mark's  and  Davis'    Steam 
Tables  are  used : 

Design  a  nozzle  taking  dry  and  saturated  steam  at  100  pounds  and 
discharging  1  pound  per  second,  against  a  pressure  of  20  pounds  absolute. 


FIG.  95. — Another  form  of  turbine  nozzle,  having  a  cylindrical  throat. 


The  entropy  of  steam  of  100  pounds  pressure  is  1.6020.  Since  the  expan- 
sion in  the  nozzle  is  adiabatic,  the  entropy  of  the  steam  coming  from  the 
nozzle  will  be  the  same.  The  entropy  of  the  liquid  at  20  pounds  absolute 
is  0.3355.  The  difference,  or  1.2665,  is  the  entropy  of  vaporization  of 
the  wet  steam  coming  from  the  nozzle.  The  quality  of  the  steam  coming 


ART.  202  ALTERNATE  METHODS  OF  DESIGNING  A  TURBINE  NOZZLE  185 

from  the  nozzle  may  be  found  by  dividing  this  quantity  by  the  entropy 
of  vaporization  of  dry  steam  of  20  pounds  pressure  and  is 

90.8  per  cent. 

The  total  heat  of  steam  of  100  pounds  pressure  is  1186.3  B.T.U.  The 
total  heat  of  the  wet  steam  at  20  pounds  pressure  is  found  by  the  formula 

H2  =  h  +  qL  and  is  196.1  +  90.8X960.0=1068.1  B.T.U. 

The  difference,  or  118.2  B.T.U.  is  the  quantity  of  heat  transformed  into 
kinetic  energy  in  the  nozzle,  a  quantity  previously  designated  by  the 
symbol  AH.  Substituting  in  the  formula 


we  will  have  2435  feet  per  second  for  the  velocity  of  the  steam  issuing 
from  the  nozzle.  The  specific  volume  of  the  steam  may  be  found  from 
its  quality  and  will  be  20.08X0.908=  18.23.  Dividing  this  by  the  velocity 
of  the  steam,  we  will  have  for  the  area  of  the  mouth  of  the  nozzle  required 
to  discharge  1  pound  of  steam  per  second,  0.0075  square  feet  or  1.08 
square  inches. 

The  pressure  of  the  steam  in  the  throat  of  this  nozzle  will  be  58  pounds. 
We  may  by  the  process  already  employed,  find  the  area  of  the  throat 
of  the  nozzle  when  it  is  required  to  discharge  1  pound  of  steam  per 
second.  The  entropy  of  the  liquid  at  58  pounds  is  0.4242.  The  entropy 
of  vaporization  will  be  1.1178.  The  quality  of  steam  will  be 


Il==  96.4  per  cent. 

The  total  heat  will  be 

259.8  +  916.5X96.4-1143.3. 
The  heat  drop  will  be 

1183.3-1143.3  =  40  B.T.U. 
The  velocity  of  the  jet  at  the  throat  will  be 

223.6V  J#=  1413  ft.  per  sec. 
The  specific  volume  of  the  steam  passing  the  throat  of  the  nozzle  will  be 

96.4X7.45  =  7.13. 
The  area  of  the  throat  will  be 

. 


186 


THE  STEAM  TURBINE 


ART.  203 


203.  Efficiency    of   Turbine   Nozzles.     The    efficiency    of    a    turbine 
nozzle  is  found  by  dividing  the  kinetic  energy  actually  realized  by  the 
energy  theoretically  developed  from  the  given  pressure  drop.     On  account 
of  the  friction  of  the  steam  against  the  walls  of  the  nozzle,  and  also  on 
account  of  the  eddying  produced  when  the  nozzle  is  of  improper  form, 
the  velocity  of  the  issuing  steam,  the  quantity  of  steam  discharged  and 
the  efficiency  of  the  nozzles  are  reduced.     An  improperly  designed  nozzle 
may  give  an  efficiency  as  low  as  90  per  cent  and  a  velocity  and  quantity 
of  discharge  of  about  95  per  cent  of  the  theoretical  value.     A  properly 
designed  nozzle  expanding  steam  between  the  pressure  limits  for  which  it 
was  designed,  ought  to  give  an  efficiency  of  more  than  97  per  cent,  and 
such  an  efficiency  has  been  realized  by  a  nozzle  of  the  form  shown  in 
Fig.  95. 

204.  The  Design  of  Turbine  Vanes.    After  the  steam  has  been  expanded 
in  the  nozzle,  it  is  necessary  to  extract  its  kinetic  energy  by  causing  it 


FIG.  96. — Properly  and  improperly  formed  vane  surfaces. 

to  strike  upon  a  moving  surface.  Its  energy  is  usually  utilized  by 
causing  it  to  strike  upon  a  series  of  vanes  (also  termed  blades  and  buckets) 
fixed  upon  the  rim  of  a  revolving  disk  or  drum  (which  is  often  termed  a 
rotor).  The  form  and  motion  of  the  surface  upon  which  the  jet  strikes 
should  be  such  that  the  steam  will  be  taken  up  smoothly  and  brought 
to  some  lower  velocity  without  shock  or  eddying.  This  result  will  be 
achieved  if  the  surface  of  the  vane  is  suitably  curved,  and  the  steam  enters 
the  vane  in  such  a  manner  that  the  direction  of  its  motion  relative  to  the 
vane  is  tangent  to  the  curved  surface  of  the  vane  at  the  entering  edge, 
as  shown  in  Fig.  96  a.  If,  however,  the  vane  is  not  properly  curved,  or 
if  the  jet  strikes  obliquely  upon  its  surface,  there  will  be  more  or  less 


ART.  205  CLASSIFICATION  OF  UMPULSE  TURBINES  187 

eddying  of  the  steam  at  the  point  of  impact  and  some  of  the  kinetic 
energy  developed  in  the  nozzle  will  be  lost  by  being  re  transformed  into 
heat.  The  effect  of  such  oblique  impact  may  be  seen  in  Fig.  96  b. 

Since  the  vanes  are  moving  as  the  steam  enters  them,  the  effect  of 
this  motion  must  be  considered.     Referring  to  Fig.  97,  line  a-b  represents 
by  its  length  and  direction  the  absolute  velocity  and  direction  of  motion 
of  the  entering  jet  of  steam. 
Line  c-d  represents  by  its 
length    and    direction    the 
velocity   and    direction    of 
motion  of  the  moving  vanes. 
The  velocity  of  the  jet  of 
steam  relative  to  any  point 
in  the  vanes  will  therefore 
be  represented  by  the  line  FIG.  97.— Velocity  diagram. 

a—e,  which  is  the  third  side 

of  the  triangle  whose  second  side,  b-e,  is  parallel  and  equal  to  c-d.  If  the 
surface  of  the  vane  has  the  form  shown  by  the  curve  /-</,  it  is  apparent  that 
the  jet  will  strike  the  vane  tangentially,  that  the  steam  will  be  taken  up 
smoothly,  without  shock,  and  its  direction  of  motion  changed  in  the  manner 
shown  by  the  arrow.  Except  for  the  effect  of  friction,  the  relative  velocity 
of  the  jet  and  the  vane  will  remain  unchanged,  and  the  steam  will  leave  the 
vane  with  a  velocity  relative  to  the  vane  which  amount  and  direction  are 
represented  by  the  length  and  direction  of  the  line  g-h  (which  is  equal 
in  length  to  a—e).  The  absolute  velocity  of  the  steam  leaving  the  vane 
will  be  represented  by  the  line  g-i,  which  is  the  third  side  of  a  triangle 
whose  second  side  is  h-i  (h-i  being  equal  and  parallel  to  c-d) .  In  conse- 
quence of  the  resulting  change  in  the  absolute  velocity  of  the  steam  its 
kinetic  energy  will  be  reduced,  the  amount  of  energy  imparted  to  the 
vanes  in  each  second  being  equal  to  the  difference  between  the  initial 
and  final  kinetic  energy  of  the  steam  discharged  per  second  by  the  nozzle. 

205.  Classification  of  Impulse  Turbines.  Impulse  turbines  are  class- 
ified as  single  stage  and  multi-stage.  A  single  stage  turbine  is  one  in  which 
the  entire  pressure  drop  occurs  in  one  set  of  nozzles.  A  multi-stage 
turbine  is  one  in  which  only  a  portion  of  the  pressure  drop  occurs  in  each 
set  of  nozzles,  the  steam  flowing  successively  through  two  or  more  sets 
of  nozzles.  An  impulse  turbine  may  use  one  row  of  vanes  per  stage  to 
take  up  the  energy  of  the  jet,  or  it  may  have  two  or  more  rows  of  moving 
vanes  with  stationary  guide  vanes  interposed  between  each  pair  of  mov- 
ing rows/  The  De  Larval  turbine  is  a  single  stage  turbine  with  a  single 
row  of  moving  vanes.  The  Kerr  turbine  is  a  multi-stage  machine  Vith 
a  single  row  of  buckets  in  each  stage.  The  Curtis  turbine  is  a  multi- 
stage machine  having  several  rows  of  vanes  per  stage.  The  simplest 


188 


THE  STEAM  TURBINE 


ART.  205 


form  is,  of  course,  the  De  Laval  turbine,  employing  a  single  pressure  stage 
and  a  single  row  of  vanes.  In  order  that  the  turbine  shall  have  a  high 
efficiency,  it  is  necessary  that  the  form  and  speed  of  the  vanes  shall  be 
such  that  the  steam  is  brought  almost  to  complete  rest.  This  requires 
that  the  vanes  shall  travel  at  very  nearly  one-half  the  velocity  of 'the  steam 
when  only  one  row  of  moving  vanes  is  employed.  Since  the  velocity 
of  the  steam  jet  ranges  from  2700  to  4500  feet  per  second,  it  will  be  seen 
that  the  vanes  of  the  De  Laval  turbine  must  travel  at  peripheral  speeds 
from  1300  to  2200  feet  per  second,  in  order  to  realize  the  full  efficiency 
which  it  is  possible  to  obtain  from  the  steam.  The  De  Laval  turbine 
is  so  constructed  that  the  vanes  may  run  at  these  high  speeds.  The 
rotational  speeds  resulting  are,  however,  entirely  too  high  for  driving 


FIG.  98. 

ordinary  machinery,  and  accordingly,  double  helical  gearing  like  that 
shown  in  Fig.  98  is  employed  to  reduce  the  speed  to  a  suitable  value. 
Since  it  is  difficult  to  construct  such  turbines  in  units  of  large  size,  the 
single  stage  De  Laval  turbines  are  built  only  in  units  of  comparatively 
small  power. 

It  is  apparent,  that  if  some  method  can  be  employed  whereby 
the  speed  of  the  moving  vanes  may  be  reduced  without  reducing  the 
efficiency  of  the  turbine,  it  will  be  desirable  to  dispense  with  speed 
reduction  gearing.  This  may  be  accomplished  by  reducing  the  velocity 
of  the  steam  jet  or  by  using  several  rows  of  vanes  in  such  a  manner  that 
each  row  abstracts  only  a  portion  of  the  velocity  of  the  steam  jet.  Both 
of  these  methods  of  speed  reduction  may  be  and  often  are  combined 
in  thfe  same  machine.  When  more  than  one  row  of  moving  vanes  are 
employed,  the  steam  leaving  the  first  set  of  moving  vanes  is  directed  by 
a  set  of  stationary  vanes  against  a  second  set  of  moving  vanes.  The 


ART.  206    DESIGN  OF  VANES  FOR  MULTI-STAGE  IMPULSE  TURBINE     189 


steam  may  then  be  directed  by  a  second  set  of  stationary  vanes  against 
a  third  set  of  moving  vanes,  and  this  action  repeated  as  many  times  as 
may  be  necessary.  When  this  is  done,  each  of  the  moving  vanes  extracts 
from  the  steam  a  portion  of  its  velocity,  and  the  peripheral  velocity 
of  the  vanes  may  be  greatly  reduced.  The  use  of  several  rows  of  vanes 
in  this  manner  considerably  decreases  the  efficiency  of  the  turbine  on 
account  of  the  eddying  resulting  from  the  repeated  reversals  tff  the  direc- 
tion of  the  current  of  steam,  and  the  friction  resulting  from  the  increase 
in  the  vane  surface.  On  the  other  hand,  the  peripheral  velocities  obtained 
are  so  much  smaller  than  those  gotten  when  a  single  row  of  vanes  is  used, 
that  it  is  practicable  to  construct  this  type  in  the  largest  sizes  and  to  use 
it  for  driving  many  kinds  of  machinery  without  reduction  gearing. 

206.  Design  of  Vanes  for  a  Multi-stage  Impulse  Turbine.  In  design- 
ing the  vanes  for  a  turbine  of  this  type,  a  velocity  diagram  may  be  used 
similar  to  that  used  for  turbines 
employing  a  single  row  of  moving 
vanes.  Such  a  diagram  is  shown  in 
Fig.  99,  in  which  a-b  represents  the 
direction  and  velocity  of  the  steam 
coming  from  the  nozzle,  b-c  is 
equal  to  the  velocity  of  the  mov- 
ing vanes,  a-c  is  the  relative 
velocity  of  the  steam  entering  the 
first  set  of  moving  vanes,  c-d,  which 
is  equal  to  a-c,  is  the  relative 
velocity  of  the  steam  leaving  the  first 
row  of  moving  vanes,  d—e  equals 
b-c,  c-e  is  the  absolute  velocity  of 
the  steam  leaving  the  first  set  of  mov- 
ing vanes,  e-f  represents  the  velocity 
and  direction  of  the  steam  leaving 
the  first  set  of  stationary  vanes, 
f-g  equals  b-c,  e-g  is  the  relative 

velocity  of  the  steam  entering  the  second  row  of  moving  vanes,  g-h 
equals  e-g  and  is  the  relative  velocity  of  the  steam  leaving  the  second 
set  of  moving  vanes,  h-i  equals  b-c,  and  g-i  represents  the  absolute 
velocity  of  the  steam  leaving  the  second  set  of  moving  vanes.  The  remain- 
der of  the  diagram  determines  in  like  manner  the  velocity  and  direction 
of  the  current  of  steam  as  it  passes  through  the  third  and  fourth  set  of 
moving  vanes. 

The  form  of  velocity  diagram  shown  in  Fig.  99  makes  no  allowances 
for  friction.  If  it  is  assumed  that  the  steam  in  its  passage  through  a 
set  of  vanes  loses  a  certain  per  cent  of  its  velocity  by  friction,  then  the 


FIG.  99. — Velocity  diagram  for  four  rows 
of  moving  vanes. 


190 


THE  STEAM  TURBINE 


AHT.  206 


velocity  of  the  steam  coming  from  the  set  of  vanes  will  be  less  than  the 
velocity  of  the  steam  entering  that  set  by  the  per  cent  of  loss  due  to  fric- 
tion. The  diagram  may  therefore  be  modified  to  take  account  of  fric- 
tion in  the  following  manner:  Assume  that  10  per  cent  of  the  velocity 
is  lost  in  friction  each  time  the  current  of  steam  passes  through  a  set  of 
vanes.  Then  the  diagram  will  have  the  form  shown  in  Fig.  100,  in  which 

c-d  is  90  per  cent  of  a-c,  e-f  is  90 
per  cent  of  c-e,  g-h  is  90  per  cent 
of  e-g  and  so  on  for  the  remainder 
of  the  diagram. 

The  vanes  are  usually  of  the 
form  shown  in  section  in  Fig.  lOla. 
The  surface  a—e-d  upon  which  the 
steam  strikes,  is  usually  the  arc 
of  the  circle,  although  it  may  be 
any  smooth  curve,  and  the  back 
a-b-c—d,  consists  of  a  circular  arc 
b—c  tangent  to  two  straight  lines 
a-b  and  c-d.  Assume  the  steam 
to  enter  in  such  a  manner  that 
its  real  direction  of  motion  is 
shown  by  the  lines.  The  form 
of  the  blade  is  then  made  such 
that  the  line  a-b  is  made  parallel 
with  the  lines.  It  follows  that 

the  steam  cannot  enter  the  surface  of  the  vane  tangentially,  but  strikes 
it  in  the  manner  shown  in  Fig.  101  a.  While  this  is  somewhat  objection- 
able, it  would  be  more  objectionable  for  it  to  strike  upon  the  back  of 
the  vane  in  the  manner  shown  in  Fig.  101  b,  and  so  retard  the  forward 
motion  of  the  blade.  The  current  of  steam  leaves  the  vane  in  the 
direction  shown  by  the  cover  lines  which  are  tangent  to  the  face  a-er-d 
at  point  d.  In  the  case  of  a  stationary  vane,  a  similar  form  is  to  be 
employed,  the  steam  entering  in  a  direction  tangent  to  the  back  of  the 
vane  and  leaving  it  in  a  direction  tangent  to  the  face.  The  forms  of 
the  van  are  thus  derived  directly  from  the  velocity  diagram. 

After  the  steam  leaves  the  nozzles  of  an  impulse  turbine,  its  pressure 
remains  constant.  In  consequence  of  its  action  upon  the  moving  vanes, 
its  velocity  is  reduced  as  it  passes  from  row  to  row  of  blading,  as  shown 
by  the  arrow  in  Fig.  101  c.  If  there  were  no  fluid  friction,  the  specific 
volume  of  the  steam  would  remain  constant  in  passing  through  the 
blading  of  any  stage.  Since,  however,  the  heat  content  of  the  steam 
is  increased  by  friction  and  eddying,  its  specific  volume  will  slightly 
increase  as  the  steam  passes  the  successive  rows  of  vanes.  It  is  neces- 


FIG.  100. — Velocity  diagram  corrected  for 
friction  loss. 


AKT.  207    DETERMINATION  OF  THE  PRESSURE  AND  ENERGY  DROP    191 

sary  that  the  area  of  the  passage  through  which  the  current  of  steam 
flows  shall  always  be  sufficient  to  carry  the  entire  quantity  of  steam 
flowing,  at  the  velocity  which  it  has  while  passing  the  point  in  question. 
In  flowing  through  the  first  set  of  vanes,  the  steam  has  a  very  high 
velocity.  In  passing  through  the  last  set  of  vanes,  it  has  a  compara- 
tively low  velocity  and  its  specific  volume  is  slightly  larger.  Consequently, 
the  area  of  the  steam  passage  through  the  last  set  of  vanes  must  be 
much  greater  than  that  through  the  first  set.  This  is  usually  accom- 
plished by  making  each  successive  row  of  vanes  longer  than  the  pre- 


ccccc 


FIG.  101  c 


FIG.  101. 

ceding,  the  heights  of  vanes  being  practically  inversely  proportional  to 
the  velocity  of  the  steam  passing  through  them. 

207.  Determination  of  the  Pressure  and  Energy  Drop  in  Multi-Stage 
Impulse  Turbines.  When  steam  passes  through  a  multi-stage  turbine  its  entropy 
does  not  remain  constant.  In  passing  through  the  nozzles  it  undergoes  adiabatic  expan- 
sion, but  when  it  issues  into  the  vanes,  eddying  and  friction  transform  a  portion  of  its 
kinetic  energy  into  heat,  increasing  its  entropy.  Let  AH  equal  the  heat  drop  result- 
ing from  adiabatic  expansion  between  the  initial  and  condenser  pressure.  Let  E 
equal  the  efficiency  of  the  turbine,  expressed  as  a  per  cent  of  the  efficiency  of  a  perfect 
turbine,  a  quantity  which  may  be  found  from  the  expression 


192  THE  STEAM  TURBINE  ART.  207 

in  which  S  is  the  probable  steam  consumption  of  the  turbine  in  pounds  per  brake 
horse-power  per  hour.  Let  n  equal  the  number  of  stages.  Then,  if  E  be  very  nearly 
unity,  and  the  steam  passes  through  the  turbine  without  appreciable  increase  in 

AJ-f 

entropy,  the  heat  drop  per  stage  will  be  .     The  pressure  of  the  steam  entering 

ITT 

any  stage  may  be  found  by  subtracting  the  quantity  from  the  total  heat  of  the 

steam,  as  it  enters  the  nozzles  of  the  preceding  stage,  and  finding,  by  means  of  a 
temperature-entropy  table,  or  a  total  heat-entropy  diagram,  the  pressure  of  steam 
having  the  total  heat  so  found,  and  the  original  entropy.  For  instance,  if  the  heat 
content  of  steam  entering  any  stage  is  1161  B.T.U.,  its  entropy  is  1.68  and  the  quantity 

AH 

is  50  B.T.U.,  then  the  heat  content  after  expansion  is  1111  B.T.U.     The  pressure 

n 

of  steam  whose  total  heat  is  1111  B.T.U.  and  whose  entropy  is  1.68,  is  found  from 
the  temperature-entropy  table  to  be  17.52  pounds  per  square  inch,  which  is  the 
pressure  of  the  steam  entering  the  next  stage. 

Usually  the  efficiency  of  a  turbine  will  range  from  55  to  80  per  cent.     In  such  a 
case  the  heat  drop  per  stage  may  be  found  by  the  empirical  equation 


The  heat  content  of  the  steam  aftar  expansion  in  the  nozzles  will  be 


in  which  Hl  is  the  total  heat  of  the  steam  entering  the  nozzles,  and  H2'  is  the  total 

heat  as  it  leaves  the  nozzles.      The  pressure  of  the  steam  leaving  the  nozzles  is,  of 

course,  fixed  by  the  quantity  H2'  and  the  entropy  of  the  steam  as  it  enters  the  nozzles. 

The  quantity  of  heat  restored  to  the  steam  by  eddying  and  friction  is  equal  to 


n 
and  the  heat  content  of  the  steam  after  it  passes  through  the  blading  will  be 


The  entropy  of  the  steam  entering  the  next  stage  will  be  fixed  by  the  pressure  of  the 
steam  already  found,  and  the  quantity  H2.  • 

The  following  problem  will  illustrate  the  method  of  designing  a  multi-stage  turbine: 
Assume  that  the  initial  steam  pressure  is  164.8  pounds  per  square  inch,  that  the  final 
pressure  is  1  pound  per  square  inch,  that  the  steam  is  initially  dry  and  saturated, 
that  the  number  of  stages  is  2  and  the  efficiency  E  is  60  per  cent.  The  initial  entropy 
is  1.56.  The  total  heat  at  the  same  entropy  and  terminal  pressure  is  87.1  B.T.U. 
The  difference,  or  322.2  B.T.U.,  is  the  heat  drop,  AH.  The  heat  drop  per  stage  will 
then  be 

322'2  '  1  +  .00057  ( ^,- )  322.2(1  -  .60) )  =  167.0  B.T.U. 


.2(1  -  .60))  = 


The  heat  content  of  the  steam  as  it  issues  from  the  nozzle  of  the  first  stage  will  there- 
fore be  1193.3-167.0-1026.3  B.T.U.  Steam  of  1.56  entropy  having  this  heat 
content  has  a  pressure  of  16.86  pounds  per  square  inch.  The  nozzles  of  the  first  stage 
are  therefore  designed  to  discharge  the  required  quantity  of  steam  and  to  operate' 


ART.  208 


THE  IMPULSE  REACTION  TURBINE 


193 


between  165  pounds  and  16.86  pounds  per  square  inch.     After  passing  through  the 
blading  the  heat  content  of  the  steam  will  be 

_™«      .60X322.2 


1193.3- 


1096.6  B.T.U. 


The  entropy  of  steam  of  16.86  pounds  pressure  and  having  a  total  heat  of  1096.6  B.T.U  . 
is  1.663.  The  total  heat  of  the  steam  issuing  from  the  nozzles  of  the  second  stage 
will  be  1096.6-167.0  =  929.6  B.T.U.  The  pressure  of  steam  of  this  heat  content 
and  1.633  entropy  is  1  pound.  The  nozzles  of  the  second  stage  will  be  designed  to  pass 
the  same  quantity  of  steam  as  will  be  passed  by  the  nozzles  of  the  first  stage  and  to 
operate  between  the  pressure  limits  of  16.36  pounds  and  1  pound  absolute.  Since 
the  steam  enters  the  nozzles  of  the  second  stage  with  low  velocity  and  its  final  velocity 
as  it  issues  from  these  nozzles  is  the  same  as  it  was  when  it  issued  from  the  nozzles 
of  the  first  stage,  and  since  the  specific  volume  of  the  steam  at  low  pressure  is  much 
greater  than  it  was  at  the  high  pressures  used  in  the  first  stage,  the  cross-sectional 
area  of  the  nozzles  of  the  second  stage  will  be  much  larger  than  that  of  those  of  the 
first  stage. 


FIG.  102. — Westinghouse-Parsons  turbine  of  an  early  type,  with  the  top  of  the  casing 

removed. 

208.  The  Impulse  Reaction  Turbine.  When  a  reaction  turbine  of 
the  Avery  type  is  used,  the  centrifugal  force  of  the  steam  contained  in  the 
revolving  element  increases  its  pressure  and  consequently  its  velocity, 
as  it  issues  from  the  nozzle.  This  increased  velocity  in  turn  increases 
the  centrifugal  force,  which,  in  its  turn,  again  increases  the  velocity  of 
the  issuing  steam.  In  order  that  such  a  turbine  shall  run  with  perfect 
efficiency,  transforming  all  of  the  available  heat  into  work,  it  is  therefore 
necessary  that  the  arms  shall  revolve  at  infinite  speed,  which  is  of  course 
impossible.  No  arrangement  of  parts  or  division  into  stages  will  elim- 
inate the  necessity  of  operating  the  rotor  at  excessive  speeds  in  order 


194 


THE  STEAM  TURBINE 


ART.  208 


to  secure  reasonable  efficiency.  Consequently,  pure  reaction  turbines 
are  no  longer  built.  By  combining  the  principles  of  the  impulse  and  the 
reaction  turbines,  as  is  done  in  the  Parsons  turbine,  illustrated  in  Fig. 
102,  a  very  efficient  mechanism  may  be  obtained.  The  blading  of  such 
turbines  consists  of  alternate  rows  of  stationary  and  moving  vanes,  as 

shown  in  Fig.  103.  The 
moving  vanes  are  cross- 
hatched  and  the  stationary 
vanes  are  blackened  in  the 
figure.  On  account  of  the 
difference  in  pressure  at  the 
two  ends  of  the  turbine,  the 
steam  flows  through  the 
blading  with  high  velocity, 
expanding  as  it  flows.  The 


FIG.  103. — Vane  sections  for  an  impulse-reaction 
turbine. 


passages  between  the  sta- 
tionary blades  act  as  fixed 
nozzles,  while  those  between 

the  moving  vanes  act  as  moving  nozzles.     The  steam  gains  in  absolute 

velocity  in  passing  through  a  row  of  stationary  vanes,  and  impinges  upon 

the  following  row  of  moving  varies,  driving  them  forward  by  its  impulse, 

As  it  passes  through  the  row  of  moving  vanes,  it  gains  in  relative  velocity. 

and  again  drives  them  forward  by  the  reaction  of  its  discharge.     The 

velocity    diagram    of    such   a 

turbine  is  shown  in  Fig.   104. 

The  velocity  of  the  steam  as 

it  issues  from   a   row  of  fixed 

vanes   is    represented   by   the 

line    a-b,    b-c    represents   the 

velocity  of  the  moving  vanes, 

and  a—c  represents  the  relative 

velocity  of  the  steam  and  the 

vanes.     The  relative  velocity  f 

of  the  steam  issuing  from  the 

moving  vanes  is  c—d,   and  its 

absolute  velocity  is  represented 

by  the  line  c-e,  d-e  being  equal 

to  b—a.     In  consequence  of  the 

pressure  drop,  this  velocity  increases  to  the  value  fy  in  passing  through 

the  next    row    of    fixed    vanes.     The    steam    continues    to    pass    from 

row  to   row   of    varies,    increasing    in    absolute    velocity   while    passing 

through  the  stationary  vanes,  and  decreasing  in  absolute,  but  increasing 

in  relative  velocity,  while  passing  through  the  moving  vanes. 


FIG.  104. — Velocity  diagram  for  an  impulse- 
reaction  turbine. 


ART.  209       METHODS  OF  GOVERNING  THE  STEAM  TURBINE  195 

The  design  of  an  impulse  reaction  turbine  is  a  much  more  complicated 
and  tedious  process  than  the  design  of  an  impulse  turbine.  For  the 
proper  methods  of  designing  such  a  turbine,  the  reader  is  referred  to  any 
of  the  standard  works  on  Steam  Turbines.  An  excellent  treatment  of 
the  subject  will  be  found  in  Roe's  "  Steam  Turbines/'  pages  54  to  72. 

Many  special  forms  of  the  steam  turbine  are  in  use  which  cannot  be 
described  in  a  work  of  this  kind.  In  principle  they  all  belong  to  one  or 
another  of  the  classes  described,  but  differ  in  their  mechanical  arrangements. 

209.  Methods  of  Governing  -the  Steam  Turbine.  Three  methods 
are  in  use  for  governing  the  steam  turbine.  The  first  method  consists 
in  throttling  the  pressure  of  the  steam  at  entrance.  This  reduces  the 
quantity  of  steam  which  flows  through  the  nozzles,  and  in  a  greater  degree 
it  reduces  the  work  performed  by  the  turbine.  Its  effect  is  somewhat 
similar  to  the  effect  of  a  throttling  governor  upon  the  steam  engine.  Re- 
ducing the  pressure  of  the  entering  steam  changes  the  pressure  in  each 
of  the  stages  of  the  turbine, -changes  the  velocity  with  which  steam  enters 
the  buckets,  and  reduces  the  efficiency  of  the  turbine,  for  if  the  turbine  is 
properly  designed  for  full  steam  pressure,  the  form  of  the  nozzle,  the  shape  of 
the  blading,  and  the  velocity  of  the  rotating  parts  will  all  be  incorrect  for 
the  reduced  pressure  which  results  from  throttling.  The  turbine  will  there- 
fore operate  at  much  lower  efficiency  at  low  load  than  it  does  at  full  load. 

The  second  method  of  governing  the  steam  turbine  is  to  admit  the  steam 
intermittently.  A  balanced  valve  in  the  pipe  supplying  steam  to  the 
turbine  is  opened  an  instant  and  then  quickly  closed,  the  action  occurring 
at  regular  intervals.  While  it  is  open  steam  passes  freely  through  the 
turbine,  and  its  operation  is  normal.  When  it  is  closed,  the  pressure  of 
the  steam  throughout  the  turbine  immediately  drops  to  back  pressure 
and  the  turbine  continues  to  revolve  until  the  next  blast  of  steam  is 
admitted.  While  the  turbine  is  receiving  steam,  it  is  working  at  maximum 
efficiency.  While  it  is  not  receiving  steam,  it  is  revolving  without  loss 
except  that  due  to  the  passage  of  the  blades  through  the  steam  at  very 
low  pressure.  The  blast  of  steam  is  admitted  to  the  turbine  from  60  to 
MO  times  per  minute,  the  duration  of  the  blast  being  determined  by  the 
governor.  When  the  load  is  light,  the  pressure  variation  in  the  first  stage 
will  have  the  form  shown  in  Fig.  105  a;  when  the  load  is  heavy,  it  will  have 
the  form  shown  in  Fig.  105  6;  and  when  the  turbine  is  overloaded,  the 
steam  is  admitted  continuously.  This  method  of  regulation  is  much 
superior  to  regulation  by  throttling,  and  the  great  inertia  of  the  revolving 
parts  prevents  any  perceptible  variation  in  speed,  in  spite  of  the  inter- 
mittent character  of  the  force  applied  to  the  turbine  blading. 

A  third  method  of  turbine  governing  consists  in  providing  each  stage 
with  the  same  number  of  nozzles,  or  groups  of  nozzles,  and  admitting 
full  steam  to  as  many  groups  as  may  be  necessary  in  order  to  carry  the 


196  THE  STEAM  TURBINE  ART.  210 

load.  Turbines  of  large  sizes  are  ordinarily  equipped  with  six  or  eight 
groups  of  nozzles  per  stage.  At  low  loads  only  a  small  part  of  the  nozzles 
will  be  open  to  the  admission  of  steam,  while  at  heavy  loads  almost 
all  the  nozzles  will  be  open,  and  when  the  turbine  is  running  at  the  limit 
of  its  capacity  all  of  the  nozzles  will  be  in  operation.  This  method 
of  governing  has  no  advantage  over  the  system  of  intermittent  admis- 
sion, and  cannot  be  applied  to  impulse  reaction  turbines.  It  is,  however, 
easy  to  apply  it  to  pure  impulse  turbines,  particularly  when  the  num- 
ber of  stages  is  small.  Most  impulse  turbines  are  governed  in  this 
manner,  while  impulse  reaction  turbines  are  usually  governed  lay  inter- 
mittent admission. 


FIG.  105  a. 


FIG.  105  6. 

210.  Efficiency  of  the  Steam  Turbine.  The  steam  turbine  operates 
upon  the  Rankine  cycle  with  complete  expansion  of  the  steam.  Since 
it  uses  a  much  more  efficient  cycle  than  the  steam  engine,  it  rriight  be 
inferred  that  the  steam  turbine  would  be  much  more  efficient  than  the 
steam  engine.  Such  is  not  the  case.  The  efficiency  of  the  two  types  of 
apparatus,  as  measured  by  the  heat  consumption  required  per  brake 
horse-power  per  hour,  is  practically  the  same,  the  steam  engine  being 
slightly  more  economical  than  the  steam  turbine  for  the  same  temperature 
range.  Since  the  form  of  cycle  employed  in  the  steam  engine  does  not 
utilize  the  lower  part  of  the  temperature  range  to  good  advantage,  it 
follows  that  the  steam  engine  can  use  high  pressure  steam  more  efficiently 
than  the  steam  turbine,  while  on  the  other  hand  the  steam  turbine  can 
use  low  pressure  steam  more  efficiently  than  the  steam  engine.  Con- 
sequently, when  the  steam  is  supplied  to  a  steam  engine  at  high  pressure 
and  superheat,  and  this  engine  discharges  this  steam  at  or  about  atmos- 
pheric pressure  into  a  steam  turbine  which  expands  it  down  to  the  lowest 
practicable  condenser  pressure,  the  efficiency  of  the  entire  plant  will  be 
greater  than  it  would  be  were  a  steam  engine  or  a  steam  turbine  alone 
employed.  Such  a  combination  of  units  has  been  adopted  in  the  Inter- 
borough  Power  Station  in  New  York  city,  in  which  a  7500  K.W.  compound 
engine  discharges  its  exhaust  into  a  steam  turbine  of  approximately  equal 
power.  The  efficiency  of  the  combined  unit  is  about  25  per  cent  greater 
than  the  efficiency  of  the  engine  when  it  is  operated  as  a  condensing  engine. 

The  following  table  will  serve  to  show  the  efficiency  of  large  steam 
engines  and  steam  turbines  for  different  conditions  of  operation : 


210 


EFFICIENCY  OF  THE  STEAM  TURBINE 


197 


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198  THE  STEAM  TURBINE  ART.  210 


PROBLEMS 

1.  Dry  and  saturated  steam  enters  a  turbine  nozzle  at  a  pressure  of  100  Ibs.  per 
square  inch.     The  nozzle  discharges  into  a  pressure  of  2  Ibs.  per  square  inch.      Find 
the  theoretical  velocity  of  the  steam  discharged.  Ans.     3560  ft.  per  sec. 

2.  Dry  and   saturated    steam   at    150   Ibs.   enters  a  turbine  nozzle.      Find  the 
pressure  and  velocity  of  the  steam  in  the  throat  of  the  nozzle. 

Ans.     87  Ibs.  and  1470  ft.  per  sec. 

3.  Design  a  turbine  nozzle  taking  dry  and  saturated  steam  at    20   Ibs.    pressure 
and  discharging  it  at  2  Ibs.  pressure.     The  entering  velocity  of  the  steam  is  100  ft. 
per  second.     Use   Peabody's  temperature-entropy  table   if   available   and   design  a 
nozzle  having  constant  acceleration. 

4.  Design  a  nozzle  for  the  conditions  in  the  preceding  problem,  making  it  of  the 
form  shown  in  Fig.  94,  using  the  methods  outlined  in  Art.  202. 

5.  A    four-stage    turbine  takes  steam  at   150  Ibs.  pressure  and   110°  superheat. 
The  back  pressure  is  1  Ib.  absolute.      Find  the  proper  pressure  in  each  of  the  four 
stages,  assuming  that  the  efficiency  of  the  turbine  is  75  per  cent. 

Ans.     150  Ibs.,  54.5  Ibs.,  16.9  Ibs.,  and  4.5  Ibs. 


CHAPTER  XIII 
CONDENSING   MACHINERY 

211.  Classification  of  Condensers.     There  are  in  use  with  the  steam 
engine  two   classes  of  condensers.      In  the  first  class  of  condensers  the 
steam  is  brought  into  contact  with  a  metallic  surface,  which  is  continu- 
ally cooled  by  the  application  of  cold  water  to  the  opposite  side  of  the 
metal,  and  the  condensed  steam  and  the  air  which  is  mingled  with  the 
vapor  in  the  condenser  are  removed  by  some  form  of  pump,  termed  the 
air-pump.      In  the  second  class  of  condensers  the  condensing  water  and 
the  steam  are  brought  into  direct  contact,  and  it  is  necessary  for  the  air- 
pump  to  remove  not  only  the  condensed  steam  and  the  air  which  it  has 
brought  over,  but  also  the  water  of  condensation  and  its  entrained  air. 
Condensers   of  the  first   class   are   known   as   surface   condensers.     Con- 
densers of  the    second  class  are  divided  into  jet  condensers,  barometric 
condensers,  and  ejector  condensers. 

212.  Surface    Condensers.     In    the    surface    condenser    the    cooling 
water  is  usually  caused  to  flow  through  thin-walled  metal  tubes  by  means 
of  a  pump  termed  the  circulating    pump.     These  tubes  may  be   made 
of  any  suitable  kind  of  metal,  such  as  copper,  iron  or  brass,  but  tinned 
brass  tubes    are   most   usual.      These   tubes    are  placed  within  a  metal 
shell,  usually  made  of  cast  iron,  into  which  the  steam  enters  from  the 
exhaust  pipe  of  the  engine.     Every  particle  of  steam  coming  in  contact 
with    one   of   these   tubes    is  immediately  condensed,   and  were  no   air 
present,  the  pressure  of  the  steam  would  be  that  corresponding  to  the 
temperature   of   the   outside  of  the  condenser   tubes,  since  as   soon   as 
each    bit    of   steam    is    condensed    by    contact    with    a    cold    tube,    it 
will    leave    about    the    tube  a  vacuum    into    which    other    steam    will 
rush/  so   causing  the   condensation  to  be  continuous.     Since,  however, 
the  steam  contains  some  air,  as  was  explained  in  Art.  167,  these  tubes 
are   surrounded   by   a   rarefied    atmosphere,  through   which   the   steam 
makes  its  way  with  some  difficulty,  so  that  the  temperature  of  the  steam 
in  the  condenser  is  higher  than  that  of  the  surface  of  the  condenser  tubes. 

One  of  the  fundamental  points  of  surface  condenser  design  is  to  so 
arrange  the  condensing  surfaces  that  the  blast  of  steam  which  sweeps 
over  them  from  the  exhaust  pipe  will  clear  away  the  air  surrounding 
them,  and  by  the  continual  stirring  up  of  the  vaporous  contents  of  the 

199 


200  CONDENSING  MACHINERY  ART.  213 

condenser,  bring  every  particle  of  steam  as  quickly  as  possible  into 
contact  with  the  condensing  surfaces. 

Since  the  steam  which  is  condensed  is  continually  bringing  into  the 
condenser  quantities  of  air,  it  follows  that  if  this  air  is  not  removed,  the 
pressure  within  the  condenser  will  continually  increase  and  the  efficiency 
and  power  of  the  engine  will  be  correspondingly  reduced,  until  finally 
no  advantage  will  be  obtained  from  the  condenser,  since  the  pressure 
in  the  condenser  will  be  as  great  as  the  pressure  of  the  atmosphere. 
In  order  to  avoid  this  difficulty,  the  air  must  be  removed  from  the  con- 
denser as  fast  as  it  is  introduced.  The  pump  which  removes  the  air 
is  called  the  air-pump.  In  case  it  removes  air  alone,  and  the  water  of 
condensation  is  removed  by  a  separate  pump,  it  is  called  a  dry-vacuum 
pump.  A  condenser  should  be  so  arranged  that  as  the  steam  flows  through 
it,  the  air  should  be  removed  from  that  point  of  the  condenser  most 
distant  from  the  entrance,  since  this  will  result  in  the  removal  of  the  max- 
imum quantity  of  air  in  a  given  quantity  of  vapor.  It  will  be  understood 
that  the  air-pump  not  only  removes  air,  but  also  the  vapor  or  steam 
present  in  the  condenser,  and  it  is  therefore  desirable  to  have  the  air- 
pump  draw  its  charge  from  that  portion  of  the  condenser  which  con- 
tains the  largest  proportion  of  air  in  the  vapor. 

213.  Arrangement  of  Cooling  Surface  and  Air-Pump.  The  tubes 
of  a  condenser  are  usually  about  l/2  to  1  inch  in  diameter,  and  the  water 
flows  through  them  from  one  end  to  the  other.  Condensers  are  com- 
monly made  in  the  manner  shown  in  Fig.  106,  which  is  a  diagrammatic 
cross-section  of  a  condenser.  The  steam  enters  from  the  exhaust  pipe 
at  A  and  as  it  enters,  it  encounters  the  cool  tubes,  where  it  is  condensed. 
The  current  of  steam  passes  to  the  left  along  the  tubes  and  then  back 
on  the  other  side  of  the  plate  B,  where  the  steam  and  condensed  water 
is  drawn  by  the  air  pump  through  the  outlet  C.  The  water  enters  the 
chamber  D  from  the  circulating  pump  and  flows  to  the  left  through  the 
tubes  until  it  reaches  the  chamber  E,  from  which  it  returns  through  the 
upper  rows  of  tubes  into  the  chamber  F  separated  by  the  partition  G 
from  the  chamber  D  and  leaves  by  the  outlet  shown.  It  will  be  noted 
that  the  current  of  cooling  water  is  opposite  in  direction  to  the  current 
of  steam.  The  effect  of  this  is  to  increase  the  efficiency  of  the  con- 
denser, as  will  appear  from  the  following. 

The  steam  which  enters  the  condenser  at  A  carries  with  it  some  air. 
This  comes  in  part  by  leakage  through  joints  in  the  exhaust  pipes  and 
passages,  in  part  by  leakage  around  the  piston  rod  and  valve  stems 
of  the  low  pressure  cylinder,  and  in  part  from  air  dissolved  or  intrained 
in  the  feed  water.  Since  the  condenser  is  open  from  end  to  end,  there 
is  only  a  very  slight  difference  in  pressure  between  the  inlet  and  the 
outlet.  The  amount  of  air  present  in  each  unit  of  volume  is  much 


ART.  214 


THEORY  OF  THE  SURFACE  CONDENSER 


201 


greater,  however,  near  the  outlet  than  it  is  near  the  inlet,  since  the  con- 
densation of  the  steam  occurs  at  all  points  through  the  condenser  and 
is  particularly  rapid  near  the  inlet.  Since  the  pressure  of  the  air  is  greater 
near  the  outlet  on  account  of  the  greater  amount  of  air  present,  the  pres- 
sure of  the  steam  and  therefore  its  temperature,  must  be  less  near  the 
outlet.  In  order  to  extract  the  heat  most  effectually  from  such  a  mixture 
of  steam  and  air  it  is  necessary  to  bring  the  coldest  vapor  into  contact 
with  the  coldest  condensing  water  and  the  hottest  condensing  water 
into  contact  with  the  hottest  vapor.  Hence,  the  most  efficient  surface 
condenser  will  be  that  in  which  the  steam  is  admitted  to  the  condenser 
at  the  point  where  the  condensing  water  is  discharged  and  the  conden- 
sing water  introduced  at  the  point  where  the  air  pump  takes  its  suction. 


FIG.  106. — Section  of  a  surface  condenser. 

214.  Theory  of  the  Surface  Condenser.  The  following  theory  of  the 
surface  condenser  is  based  on  the  assumption,  which  is  not  quite  fulfilled 
in  practice,  that  the  air  pressure  in  a  condenser  is  infinitesimal,  and  the 
steam  in  all  parts  of  the  condenser  is  at  the  same  temperature.  When 
water  passes  through  a  tube  surrounded  by  steam  of  a  given  temperature, 
the  steam  condenses  upon  the  outside  of  the  tube  (provided  the  water 
is  colder  than  the  steam)  and  the  water  receives  heat  by  the  process, 
consequently  increasing  in  temperature.  Assuming  a  tube  having  a 
diameter  c  in  feet,  a  length  L,  in  feet,  and  through  which  water  is  flowing 
with  the  velocity  V,  in  feet  per  second,  we  will  have  the  water  warmed 
at  a  rate  depending  upon  the  rate  of  heat  absorption.  It  is  known  that 
the  amount  of  heat  transferred  from  steam  to  water  under  these  con- 
ditions depends  upon  the  difference  in  temperature  between  the  steam 
and  water.  Let  this  difference  in  temperature  be  Tt  a  variable,  let  T8 


202  CONDENSING  MACHINERY  AKT  214 

be  the  temperature  of  the  steam  and  Tw  be  the  initial  temperature  of 
the  water.  Then  the  number  of  B.T.U.  transferred  from  the  steam  to 
the  water  through  each  square  foot  of  tube  surface  per  second  is  equal 
to  K  T,  where  K  is  a  constant  to  be  determined  experimentally. 

Let  us  assume  that  we  have  within  the  tube  a  small  volume  of  water 
whose  length  is  dL  and  whose  area  is  that  of  the  cross-section  of  the  tube. 
The  weight  of  this  small  quantity  of  water  will  be 

4 

0.7854  c2dLx 62.5  =  49. 1  c2  rfL  Ibs (1) 

If  its  temperature  in  a  given  short  increment  of  time  be  increased  by 
dT,  and  its  specific  heat  is  assumed  to  be  unity,  the  amount  of  heat 
absorbed  will  be 

49.1  dT  dL  c2  =  the  heat  absorbed (2) 

The  heat  absorbed  through  the  tube  in  the  given  increment  of  time,  dt, 
will  be  equal  to 

3.1416  cXdL  K  T  dt=the  heat  transferred.      .     .     .     (3) 

The  heat  transferred  will,  of  course,  equal  the  heat  absorbed  by  the 
water,  and  we  may  so  write  them,  or 

3.1416  cdLKT  d*  =  49.1  dT  dL  c2 (4) 

Clearing,  we  have 

dT  K 

-^  =  0.064  ±dt (5) 

Integrating  these  expressions  we  have 

rr  j 

loge  T  =  0.064  —  +  C (6) 

In  order  to  find  C,  we  may  put  t  equal  to  zero,  in  which  case  the  difference 
in  temperature  between  the  steam  and  the  water  will  be  (TS~TW}, 
since  the  water  has  received  no  addition  of  heat.  From  this  we  deduce 
that 

C  =  loge(T8-Tw),        (7) 

and 

(8) 


ART.  215  RATE  OF  HEAT  TRANSMISSION  IN  SURFACE  CONDENSERS    203 

It  may  be  noted  that  since  the  difference  in  temperature  T  is  contin- 
ually diminishing  as  the  time,  t,  increases,  the  expression  dT  is  essen- 
tially negative,  which  throws  the  equation  into  the  form  given  when 
properly  written. 

In  order  to  find  the  temperature  to  which  the  water  will  be  raised 

in  a  condenser  or  feed-water  heater,  we  may   write  ^  for  t,  which  gives 

the  length  of  time  required  for  the  water  to  traverse  the  given  length  of 
the  tube.  Substituting  this  value  for  t  we  obtain  the  temperature  differ- 
ence between  the  water  and  the  steam  after  the  water  has  traversed  the 
condenser  tube,  and  from  this  the  rise  in  temperature  and  the  quantity 
of  heat  absorbed  by  the  water  in  traversing  the  tube. 

215.  Rate  of  Heat  Transmission  in  Surface  Condensers.  Experi- 
ments by  various  engineers,  according  to  Kent,  give  for  the  rate  of  trans- 
mission of  heat  through  clean  metal  surfaces,  from  0.09  to  0.18  B.T.U. 
per  square  foot  per  second.  In  the  case  of  ordinary  metal  surfaces 
fouled  by  cylinder  and  saline  deposits,  the  conductivity  is  about  %  that 
for  clean  metal  surfaces.  If  we  substitute  the  value  given  above  for 
K  we  will  find  that  the  equation  reduces  to  the  form 


logc  T  =  loge  (T8-TW)  -  0.004  ~-  .....     (1) 

0  V 

This  equation,  for  the  purposes  of  computation,  may  be  reduced  to  the 
form 


log  T  --=  log  (77S  -  Tw)  -  0.02  --  (2) 

or  to  the  form 

logT  =  log  (77S -7^)- 0.02  ~, (3) 

in  which  T  is  the  difference  in  temperature  between  the  water  and  steam 
at  any  instant,  t  is  the  length  of  time  during  which  the  water  has  been 
;  flowing  through  the  condenser  in  seconds,  d  is  the  diameter  of  the  con- 
denser tubes  in  inches,  L  is  the  length  of  the  condenser  tube  in  feet. 
V  is  the  velocity  in  feet  per  second  for  the  water  flowing  in  the  tubes, 
T8  is  the  temperature  of  the  steam  and  Tw  is  the  initial  temperature  of 
the  water.  The  constant  given  above  is  that  which  is  proper  for  brass 
condenser  tubes  under  average  condition.  In  the  case  of  iron  tubes 
the  constant  would  be  slightly  less,  and  in  the  case  of  copper  tubes  slightly 
greater  than  0.02. 


204 


CONDENSING  MACHINERY 


ART.  21n 


If  we  plot  from  this  equation  the  relation  between  the  temperature 
of  the  water  flowing  in  the  condenser  tubes  and  the  length  of  time 
during  which  it  has  been  flowing  through  the  condenser,  as  is  done  in 
Fig.  107,  we  will  find  that  the  water  starts  at  the  temperature  Tw  and 
rapidly  increases  in  temperature  at  first.  As  t  increases,  however,  this 
rate  of  temperature  increase  becomes  less  and  less,  and  the  temperature 
finally  approaches,  but  never  reaches,  Ts.  Hence,  no  matter  how  much 
we  may  increase  the  area  of  the  condensing  surface,  we  cannot  bring 
the  temperature  of  the  condensing  water  to  the  temperature  of  the  steam. 
From  this  same  figure  it  will  also  be  seen  that  if  the  amount  of  water 
flowing  through  a  condenser  be  diminished,  the  final  temperature  of 


10(1 


r 


70 


§60 
H 


lit 


40        50        60         70 
Time  in  Seconds. 


90     100 


FIG.  107. — Relation  between  the  temperature  of  the  cooling  water  and  the  time  it 
occupies  in  passing  through  the  condenser. 

the  water  will  be  increased.  However,  since  this  increase  in  tempera- 
ture is  not  proportional  to  the  decrease  in  the  quantity  of  water  flowing, 
the  capacity  of  the  condenser  will  be  diminished.  Fig.  108  shows  the 
relation  between  the  capacity  of  the  condenser,  in  pounds  of  steam  per 
square  foot  of  cooling  surface  per  hour,  and  the  condensing  water  sup- 
plied per  square  foot  of  cooling  surface  per  hour,  at  temperatures  60° 
and  30°  below  the  steam  temperature.  An  inspection  of  these  curves 
shows  that  by  increasing  the  quantity  of  water  flowing,  we  can  increase 
the  quantity  of  steam  which  may  be  condensed  without  changing  the 
size  of  the  condenser,  but  doubling  the  quantity  of  .circulating  water 
will  not  double  the  quantity  of  steam  condensed,  although  it  will  very 
largely  increase  it. 

216.  The  Jet  Condenser.     In  the  case  of  the  jet  condenser  which  is 
illustrated  in   Fig.   109,  steam  is  introduced  into  a  receiver  (which  is 


ART.  216 


THE  JET  CONDENSER 


205 


usually  pear  shaped  in  form)  at  the  top.  Into  this  receiver  there  is 
sprayed,  usually  by  the  suction  created  by  the  air-pump,  a  supply  of 
water.  This  water  being  introduced  in  the  form  of  fine  spray  exposes 
a  large  surface  upon  which  the  steam  in  the  condenser  quickly  condenses. 
The  mingled  water  of  condensation  and  condensed  steam  are  then  with- 
drawn, together  with  the  air  which  has  been  brought  in  by  the  steam, 


ii 


10 


300       300         400        500        600        700        800 
Lbs.  oi.'  Cooling  Water  per  sq.  ft.  per  Hr. 


900     1000 


FIG.  108.— Relation  between  the  water  circulated  and  the  capacity  of  the  condenser. 

CURVE  1.  For  an  initial  temperature  difference  of  30°  between  the  steam  and  cooling 
water. 

CURVE  II.  For  an  initial  temperature  difference  of  60°  between  the  steam  and  the 
cooling  water. 

and  that  given  up  by  the  condensing  water  under  the  combined  influence 
of  heat  and  vacuum.  In  the  case  of  the  jet  condenser,  the  air-pump  must 
be  very  much  larger  than  in  the  case  of  the  surface  condenser,  in  order 
to  attain  the  same  vacuum.  No  circulating  pump  is  required  ordinarily 
with  a  jet  condenser,  the  air-pump  performing  that  service.  The  amount 
of  air  to  be  drawn  away  in  a  given  time,  in  the  case  of  a  jet  condenser 


206 


CONDENSING  MACHINERY 


ART.  217 


is  several  times  that  which  must  be  drawn  away  in  the  case  of  a  surface 
condenser  of  the  same  capacity,  since  a  considerable  proportion  of  the 
air  in  the  jet  condenser  is  that  which  is  brought  in  by  the  condensing 
water.  Where  a  high  vacuum  is  to  be  maintained  other  forms  of  conden- 
sing apparatus  are  usually  preferable  to  the  jet  condenser.  This  is  also 
true  in  those  cases  where  it  is  desirable  to  use  the  condensed  steam  as 
boiler  feed,  as  for  instance  in  marine  work,  and  stationary  power  plant 
work  when  steam  turbines  are  used.  In  the  latter  case,  since  the  steam 
turbines  do  not  require  internal  lubrication  as  do  steam  engines,  the 

exhaust  steam  carries  n6  oil  and  the  con- 
densate  is  suitable  for  boiler  feed.  In  the 
case  of  the  ordinary  reciprocating  engine, 
however,  the  cylinder  oil  in  the  exhaust 
steam  is  difficult  to  extract,  and  unless  it  is 
extracted,  the  water  of  condensation  is  not 
suitable  for  boiler  feed. 

217.  The  Ejector  Condenser.  The  ejector 
condenser  is  a  type  of  condensing  apparatus 
which  depends  upon  the  velocity  of  the 
stream  of  condensing  water  to  carry  away 
the  air  in  the  condenser.  Such  an  appa- 
ratus is  illustrated  in  Fig.  110.  The  steam 
enters  the  condenser  through  the  pipe  A. 
The  condensing  water  is  forced  into  the 
condenser  under  considerable  pressure 
through  the  pipe  B,  and  flows  into  the  body 
of  the  apparatus  at  high  velocity  in  the  form 
of  a  hollow  cone,  the  steam  condensing  upon 
its  surface.  The.  air  associated  with  the 
steam  is  swallowed  up  in  this  stream  of 
water  and  carried  past  the  throat  of  the 

condenser  in  the  form  of  innumerable  bubbles.  As  the  stream  of  con- 
densing water  and  condensed  steam  descends  through  the  tail  pipe  F, 
these  bubbles  are  carried  through,  since  the  velocity  of  the  water  in  the 
tail  pipe  is  higher  than  the  velocity  at  which  the  bubbles  ascend.  The 
condensing  water,  the  condensed  steam  and  the  entrained  air  are  finally 
discharged  into  a  well  at  the  bottom  of  the  tail  pipe.  Many  arrange- 
ments are  in  use  for  exposing  a  greater  area  of  the  condensing  water  to 
the  action  of  the  steam  and  for  regulating  the  quantity  of  water  used 
when  the  condenser  is  not  operated  at  its  capacity.  It  is  not  necessary 
that  the  condenser  should  be  set  up  at  an  elevation  in  the  manner  shown, 
since  the  placing  of  a  pump,  preferably  a  centrifugal  pump,  in  the  tail  pipe, 
will  permit  this  type  of  condenser  to  be  used  when  head  room  is  limited. 


FIG.  109.— Section  of 
denser. 


con- 


ART.  218 


THE  BAROMETRIC  CONDENSER 


207 


218.  The  Barometric  Condenser.  The  barometric  condenser  shown 
in  Fig.  Ill  differs  from  the  ejector  condenser  in  that  it  does  not  depend 
upon  the  velocity  of  the  condensing  water  to  eject  the  air,  and  from  the 
jet  condenser  in  that  the  condensing  water  is  not  removed  by  the  air- 
pump.  The  air  is  removed  by  a  separate  pump  known  as  a  dry  vacuum 
pump,  through  the  air  pipe  A.  A  tail  pipe  F,  shown  "in  the  drawing,  is 


"Water 


FIG.  110. — Diagram  of  an  ejector 
condenser. 


FIG.  111. — Section  of  a  barometric 
condenser. 


of  use  only  to  carry  away  the  condensing  water.  The  water  rises  to  such 
a  height  in  the  tail  pipe  that  it  will  flow  out  of  the  condenser  against  the 
pressure  of  the  atmosphere. 

219.  Importance  of  Good  Vacuum.  With  the  advent  of  the  steam 
turbine,  the  matter  of  high  vacuum  and  good  condensing  apparatus 
has  very  greatly  increased  in  importance.  While  the  power  of  a  compound 


208  CONDENSING   MACHINERY  ART.  220 

engine  of  the  ordinary  type  will  be  increased  only  about  four  and  one- 
half  per  cent,  by  increasing  the  vacuum  from  26  to  28  inches,  the  power 
of  a  steam  turbine  for  a  given  steam  consumption  will  be  increased  in 
most  eases  by  about  12^  per  cent.  Increasing  the  vacuum  from  28 
inches  to  29  inches  will  increase  the  power  of  steam  turbine  almost  10 
per  cent.  Since  the  excellence  of  the  vacuum  obtained  depends  upon 
the  efficiency  of  cooling  and  upon  the  efficiency  of  the  air  pump,  it  will 
be  seen  that  the  proper  design  of  condensers  and  air  pumps  is  a  matter 
of  very  great  economic  importance  in  turbine  installations. 

220.  Air  in  the  Condenser.  Water  usually  contains  about  3  per 
cent  of  air,  by  volume,  at  ordinary  temperatures,  the  volume  of  the  air 
being  estimated  as  free  air  (i.e.,  at  atmospheric  pressure  and  tempera- 
ture). It  may  also  contain  a  larger  proportion  by  volume  of  carbon 
dioxide  or  ammonia,  although  it  very  seldom  does.  These  gases  may 
be  dissolved  in  water,  or 4  they  may  be  entrained  (i.e.,  suspended  in 
the  water  in  the  form  of  fine  bubbles).  All  of  these  gases  may  be 
expelled  by  heating  the  water  to  boiling  at  atmospheric  pressure  in  an 
open  feed-water  heater.  Under  the  conditions  ordinarily  encountered 
in  condenser  practice,  we  may  expect  to  have  introduced  into  the  sur- 
face condenser  from  the  feed  water  about  1  cubic  foot  of  free  air  for 
every  30  to  100  cubic  feet  of  feed-water.  The  amount  of  air  which  enters 
the  condenser  on  account  of  leakage  when  the  exhaust  piping  and  the 
rod  packings  are  in  good  ordfer,  will  be  from  50  per  cent  to  150  per 
cent  of  that  normally  entering  with  the  feed-water.  The  air-pump  must 
therefore  be  designed  to  handle  1  cubic  foot  of  free  air  for  every  10  to 
50  cubic  feet  of  feed-water  when  it  serves  a  surface  condenser,  or  1 
cubic  foot  of  free  air  for  every  30  to  150  cubic  feet  of  condensing  water 
when  it  serves  a  jet  or  barometric  condenser. 

The  pressure  of  the  air  in  a  surface  condenser  is  usually  about  .30 
to  .50  pound  per  square  inch  absolute,  when  a  first-class  air-pump  of 
usual  proportions  is  employed.  Since  the  pressure  of  the  atmosphere 
is  14.7  pounds  per  square  inch,  it  will  be  seen  that  the  volume  of  the 
air  in  the  condenser  will  be  about  30  to  50  times  its  volume  at  atmos- 
pheric pressure.  Consequently,  if  the  usual  percentage  of  air  is  asso- 
ciated with  the  feed- water,  the  volume  of  the  air  to  be  removed  from 
a  surface  condenser  will  be  roughly  equal  to  the  volume  of  the  feed- 
water,  and  the  air-pump  must  be  proportioned  accordingly.  The  pres- 
sure in  the  condenser  will  be  equal  to  the  pressure  of  the  water  vapor, 
which  is  determined  by  its  temperature,  plus  the  pressure  of  the  air.  It 
will  be  seen  then,  that  if  the  pressure  in  the  condenser  is  to  be  reduced, 
and  a  higher  vacuum  attained,  we  may  do  so  either  by  reducing  the 
temperature  of  the  vapor  by  furnishing  a  larger  quantity  of  cooling 
water,  or  else  we  may  increase  the  capacity  of  the  air-pump  and  so 


AKT.  221 


THE  AIR-PUMP 


209 


reduce  the  pressure  of  the  air.  The  pressure  of  the  air  is  approximately 
inversely  proportional  to  the  capacity  of  the  air  pump.  In  the  case  of  a  jet 
or  barometric  condenser,  the  volume  of  the  air  removed  is  about  one-half 
the  volume  of  the  condensing  water.  Since,  however,  a  condenser 
requires  about  20  pounds  of  condensing  water  per  pound  of  feed-water 
it  will  be  seen  that  a  jet  or  barometric  condenser  will  need  a  much  larger 
air-pump  than  will  a  surface  condenser,  to  maintain  the  same  vacuum. 
It  is  possible  by  careful  workmanship  and  proper  design  of  the 
piping  system,  to  make  the  exhaust  pipe  leading  from  the  engine  or 
turbine  to  the  condenser,  air  tight.  In  the  case  of  a  properly  designed 
turbine  it  is  also  possible  to  eliminate  entirely  all  air  leakage,  although 
there  will  be  some  air  leakage  in  the  case  of  the  best  steam  engines,  around 
the  valve  stems  and  piston  rods.  In  the  case  of  a  steam  turbine  plant 
it  is  possible,  since  no  lubricating  oil  is  carried  into  the  condenser  by 
the  steam,  to  pump  the  condensed  steam  back  into  the  boiler  and  use 
it  over  and  over  again.  The  feed-water  obtained  in  this  manner  will, 
of  course,  be  free  from  air,  so  that  it 
is  practicable  in  &  first-class  steam 
turbine  plant  to  maintain  a  very 
high  vacuum  with  a  comparatively 
small  air-pump  when  a  surface  con- 
denser is  used.  When  a  jet  condenser 
is  used,  the  vacuum  will  not,  of  course, 
be  as  good  as  it  would  be  with  a 
surface  condenser,  unless  the  supply 
of  condensing  water  is  very  limited. 
In  case  the  supply  of  condensing 
water  is  limited,  it  will  be  found  that 
a  jet  condenser  will  give  a  better 
vacuum,  since  in  the  case  of  the 
jet  condenser,  the  condensing  water 
is  raised  to  the  temperature  of  the 
vapor  in  the  condenser,  while  in 
the  case  of  a  surface  condenser 
there  will  necessarily  be  a  differ- 
ence between  the  temperature  of  the 
vapor  and  that  of  the  discharged 
condensing  water. 

221.  The    Air-pump.       Air-pumps      Fia  i12._Section  of  a  wet  air  pump, 
are    of    two    classes,    wet    and    dry 

pumps.  The  wet  air  pump  removes  the  condensed  steam  or  condensing 
water  and  the  air  together.  A  section  of  such  a  pump  is  shown  in  Fig. 
112.  Since  the  valves  of  the  pump  are  so  arranged  that  they  are  always 


210 


CONDENSING  MACHINERY 


ART.  221 


covered  with  water  and  the  clearance  space  of  the  pump  cylinder  is 
filled  with  water  at  the  end  of  the  stroke,  it  will  be  seen  that  there  will 
be  no  air  in  the  clearance  space  when  the  suction  stroke  begins.  This 
is  a  matter  of  great  importance  in  air-pump  design.  If  the  clearance 
space  of  the  air-pump  is  filled  or  partially  filled  with  air  at  the  end  of 
the  stroke,  this  air,  if  it  is  to  be  expelled  at  all,  must  be  at  atmospheric 
pressure.  Consequently,  during  the  suction  stroke  of  the  pump,  this 
air  will  expand  and  prevent  the  pump  from  taking  suction  from  the 
condenser  during  the  greater  part  of  the  stroke,  which  will  very  greatly 
reduce  the  capacity  of  the  pump  for  a  given  size  of  cylinder.  By 
designing  the  pump  so  as  to  avoid  the  presence  of  air  in  the  clearance 
space  at  the  end  of  the  stroke,  this  difficulty  is  avoided. 

When  a  dry  vacuum  pump  is  used  and  the  water  is  removed  by  a 
separate  pump,  it  will  be  seen  that  it  will  be  impossible  to  use  this 

scheme  in  avoiding  the 
presence  of  air  in  the 
clearance  space.  A  dry 
vacuum  pump  may,  how- 
ever, be  constructed  with 
very  little  clearance,  much 
less  than  is  practicable  in 
the  case  of  a  wet  air  pump. 
It  may  also  run  at  a  high 
speed,  which  greatly  in- 
creases the  capacity  of  a 
given  size  of  cylinder.  Dif- 
ferent methods  are  adopted 
by  different  makers  in  order 
to  avoid  the  reduction  in 
capacity  incident  upon  the 
clearance  of  the  cylinder. 
One  method  is  to  use  two 
cylinders,  the  larger  one  of 

which  takes  its  suction  from  the  condenser,  and  discharges  into  a  receiver, 
while  the  second  one  takes  its  suction  from  this  receiver  and  discharges 
into  the  air.  It  will  be  seen  that  the  vacuum  obtainable  by  this  system 
of  operation  with  pump  cylinders  of  given  clearance,  is  much  greater 
than  can  be  obtained  by  the  use  of  a  single  cylinder  of  the  same 
clearance,  as  may  be  seen  from  the  following  consideration.  Assume  a 
clearance  of  5  per  cent.  Then  with  a  single  cylinder  air-pump,  the 
lowest  pressure  which  can  be  reached  will  be  about  1/2o  of  an  atmosphere 
when  the  quantity  of  air  entering  the  condenser  is  negligible.  This  will 
be  the  lowest  air  pressure  reached  in  the  condenser  in  the  case  of  a 


FIG.  113. — Section  of  a  dry  vacuum  pump. 


ART.  221 


THE  AIR-PUMP 


211 


FIG.  114. — Card  from  the  dry  vacuum 
pump,  shown  in  Fig.  113. 


single  cylinder  air-pump,  or  in  the  receiver  in  the  case  of  the  com- 
pound air-pump.  The  extra  cylinder  of  the  compound  air-pump  will 
reduce  the  pressure  in  the  condenser  to  l/2o  of  the  pressure  in  the 
receiver,  or  y40o  of  an  atmosphere.  If  the  quantity  of  air  entering 
the  condenser  is  appreciable,  the  air  pressure  will  of  course  be  greater 
in  both  cases  than  the  amounts  given. 
A  second  method  sometimes  used  is 
to  connect  the  clearance  space  of  the 
two  ends  of  a  double-acting  cylinder 
by  means  of  a  valve  which  is  opened 
for  an  instant  after  the  contents  of 
one  end  of  the  cylinder  have  been 
discharged  against  atmospheric  pres- 
sure. A  device  of  this  kind  is  shown  in 
Fig.  113.  The  port  P  connects  the  two 
ends  of  the  cylinder  during  the  instant 
just  following  the  discharge  of  the  contents  of  one  end,  and  previous  to  the 
beginning  of  the  compression  of  the  contents  of  the  other  end.  By  this 
means,  the  pressure  of  the  air  in  the  clearance  space  is  caused  to  fall 
to  that  of  the  opposite  end  of  the  cylinder,  so  that  the  card  given  by 
the  air-pump  has  the  form  shown  in  full  lines  in  Fig.  114,  instead  of  that 
shown  in  dotted  lines  in  the  same  figure,  which  would  be  the  form  of  card 
given  by  the  pump  if  it  did  not  have  the  auxiliary  port.  The  capacity 
of  the  pump  without  this  auxiliary  port  would  be  proportional  to 
the  distance  a-d.  By  means  of  this  auxiliary  port,  the  capacity  is 
increased  until  it  is  proportional  to  the  distance  a-c.  The  efficiency 
of  the  pump  when  measured  by  the  ratio  between  the  work  actually 
supplied  to  it  and  the  work  theoretically  required  to  remove  the  air  is 
less  with  the  auxiliary  port  than  without  it.  However,  the  advantage 
of  very  greatly  increasing  the  capacity  of  the  pump,  without  increasing 
the  size  of  the  cylinder,  makes  this  a  desirable  principle  of  con- 
struction. 

A  third  method  of  increasing  the  vacuum  obtained  by  the  use  of  a 
given  air-pump  is  to  force  the  air  from  the  main  condenser  into  a  small 
auxiliary  condenser  by  a  blast  of  steam  as  shown  in  Fig.  115.  In  this 
figure  A  is  the  main  condenser,  R  is  a  so-called  augmentor  condenser, 
and  C  is  an  aspirator  operated  by  a  steam  blast.  The  purpose  of  the 
aspirator  is  to  draw  the  air  out  of  the  main  condenser,  and  to  force  it 
into  the  augmentor  condenser  in  which  its  pressure  will  be  materially 
greater  than  in  the  main  condenser.  The  difficulty  of  removing  the  air 
from  the  augmentor  condenser,  will  of  course  be  very  much  less  than  of 
removing  it  from  the  main  condenser  in  which  the  absolute  pressure 
will  be  considerably  lower.  The  steam  used  for  the  blast  may  be  low 


212 


CONDENSING  MACHINERY 


ART.  221 


pressure  steam,  which  has  already  been  used  in  an  engine  or  turbine  and 
which  has  surrendered  the  most  of  its  potential  work. 


FIG.  115. — Section  of  a  surface  condenser  equipped  with  an  augmenter  condenser. 


PROBLEMS 

1.  Cooling  water  enters  a  surface  condenser  at  a  temperature  of  56°.     The  tem- 
perature of  the  steam  in  the  condenser  is  90°.     It  takes  four  seconds  for  the  water  to 
pass  through  the  condenser.     The  diameter  of  the  condenser  tubes  is  1  in.     What  is 
the  final  temperature  of  the  condensing  water?  Ans.     61.7°  F. 

2.  A  condenser  having  tubes  8  ft.  long  is  arranged  with  four  passes  (i.e.,  so  arranged 
that  the  water  passes  through  the  condenser  four  times,  making  its  total  travel  32  ft.). 
The  tubes  are  f  in.  diameter  and  the  velocity  of  the  water  is  H  ft.  per  second.     The 
temperature  of  the  steam  is  110°  and  of  the  entering  water  80°.     Find  the  temperature 
of  the  water  discharged  from  the  condenser.  Ans.     101.92°  F. 

3.  What  quantity  of  cooling  water  enters  each  tube  per  second  in  problem  2? 

Ans.     0.288  Ibs. 

4.  What  quantity  of  heat  is  imparted  by  the  condensing  steam  to  this  quantity 
of  water?  Ans.     6.31  B.T.U. 

5.  The  condenser   in  Problem  2  is  required  to  condense  30,000  Ibs.  of  steam  per 
hour,  having  a  quality  of  85  per  cent.     What  quantity  of  heat  must  be  absorbed  by 
the  cooling  water?  Ans.     26,250,000  B.T.U.  per  hr. 

6.  How  many  pounds  of  circulating  water  will  be  required  to  absorb  this  quantity 
of  heat  with  the  given  rise  in  temperature?  Ans.     333  Ibs.  per  sec. 

7.  How  many  tubes  will  be  required  in  each  pass  in  order  that  this  quantity  of 
water  may  be  circulated  under  the  conditions  in  Problem  2?  Ans.     1155. 

8.  What  total  area  of  cooling  surface  will  the  above  number  of  tubes  furnish? 

Ans.     7250  sq.ft. 

9.  How  many  pounds  of  wet  steam  will  be  condensed  per  square  foot  of  cooling  sur- 
face per  hour?  Ans.     4.14  Ibs. 

10.  If  the  same  number  of  tubes  are  arranged  in  a  single  pass,  what  will  be  the 
velocity  and  length  of  path  of  the  circulating  water?        Ans.     f  ft.  per  sec.  and  8  ft. 


ART.  221  PROBLEMS  213 

11.  What  will  be  the  final  temperature  of  the  circulating  water? 

Ans.     Same  as  in  Problem  2. 

12.  Why  is  the  water  usually  circulated  through  a  condenser  with  a  high  velocity 
in  spite  of  the  fact  that  the  theoretical  final  temperature  of  the  water  is  the  same  when 
it  is  circulated  at  low  velocity? 

13.  Water  is  supplied  to  a  jet  condenser  having  a  temperature  of  60°.     The  tem- 
perature of  the  steam  in  the  condenser  is  110°,  and  the  quality  of  the  steam  90  per 
cent.     How  many  pounds  of  circulating  water  must  be  supplied  per  pound  of  wet 
steam  condensed?  Ans.     18.5  Ibs. 

14.  If  the  vacuum  gage  of  the  above  condenser  shows  24  inches,  while  the  barometer 
shows  29  inches,  what  is  the  air  pressure  in  the  condenser? 

Ans.     1.19  Ibs.  per  sq.in. 

15.  What  will  be  the  reading  of  the  vacuum  gage  of  the  above  condenser,  if  the 
capacity  of  the  air-pump  is  doubled?  Ans.     25.2  in.  Hg. 


V   CHAPTER  XIV 
COMBUSTION 

222.  The  Nature  of  Combustion      Combustion,  in  the  sense  in  which 
it  is  used  in  engineering,  is  the  act  of  chemical  union  of  the  oxygen  of 
the  air  with  the  carbon  and  hydrogen  of  a  fuel,  with  an  accompanying 
evolution  of  heat  and  light.     The  fuels  commonly  used  for  the  purpose 
of  steam  generation  are  coal,  coke,  wood,  and  oils.     These  consist  of 
carbon  and  hydrogen,   together  with  traces   of  sulphur  and  phosphorus 
and  also  of  oxygen  and  inert  elements  and  compounds.     Coal  and  coke 
contain  free  carbon.     Coal,  wood,  and  oils  also  contain  compounds  of 
carbon   and   hydrogen   and   of   carbon,   hydrogen   and   oxygen.     Carbon 
and  its  compounds  are  the  sources  of  practically  all  of  the  heat  developed 
by  combustion  in  thermodynamic  apparatus. 

223.  Heat  of  Combustion.     When  a  pound  of  any  substance  is  burned 
in  oxygen,  we  find  that  a  definite  quantity  of  heat  is  evolved  as  a  result 
of  the  reaction.     This  heat  is  first  imparted  to  the  products  of  combus- 
tion, and  by  them  conveyed  to  the  bodies  in  their  neighborhood.     The 
heat  of  combustion,  as  this  quantity  is  termed,  is  expressed  in  B.T.U.  per 
pound  of  combustible.      The  heat  of  combustion  of  various  substances 
is  given  in  Table  XII  on  page  215. 

In  the  first  column  of  this  table  will  be  found  the  names  of  the  elements 
and  chemical  compounds,  commonly  found  in  fuels,  and  also  of  most 
of  the  common  fuels.  In  the  second  column  the  physical  state  of  the 
substances  at  atmospheric  pressure  and  temperature  is  given.  In  the 
third  column  will  be  found  the  chemical  symbol  of  the  substance.  In 
the  fourth  column  will  be  found  the  atomic  weight  of  the  substance,  in 
case  it  is  an  element.  In  the  fifth  column  are  given  the  molecular  weights 
of  elements  and  compounds.  In  the  sixth  column  will  be  found  the 
weight  of  the  products  of  combustion  in  pure  oxygen.  In  the  seventh 
column  are  the  chemical  symbols  of  the  products  of  combustion.  In  the 
eighth  column  is  given  the  heat  of  combustion,  assuming  that  the  prod- 
ucts of  combustion  are  reduced  to  atmospheric  pressure  and  temperature, 
and  the  steam  formed  is  condensed  to  water.  In  the  ninth  column  the 
latent  heat  at  70°  F.  of  the  steam  formed  by  the  combustion  of  1  pound 
of  the  substance  is  given.  In  column  ten  is  given  the  number  of  pounds 
of  oxygen  theoretically  required  per  pound  of  combustible.  In  column 

214 


ART.  223 


HEAT  OF  COMBUSTION 


215 


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216 


COMBUSTION 


ART.  224 


eleven  will  be  found  the  number  of  pounds  of  air  containing  this  quantity 
of  oxygen,  and  in  column  twelve  the  number  of  pounds  of  nitrogen  con- 
tained in  this  quantity  of  air.  In  column  thirteen  will  be  found  the 
water  equivalent  of  the  products  of  combustion  in  pure  oxygen,  and  in 
column  fourteen  the  water  equivalent  of  the  products  of  combustion  in 
air.  The  water  equivalent  of  a  body  may  be  denned  as  its  heat  absorb- 
ing capacity  in  B.T.U.  per  degree  rise  in  temperature,  and  may  be  found 
by  multiplying  its  mass  in  pounds  by  its  specific  heat.  The  method 
of  computing  the  quantities  in  the  table  may  be  inferred  from  the  fol- 
lowing paragraphs  on  the  combustion  of  carbon  and  hydrogen. 

It  is  sometimes  convenient  in  making  computations  on  com- 
bustion to  make  use  of  the  heat  of  formation  of  a  compound.  This 
may  be  defined  as  the  quantity  of  heat  evolved  in  forming  a  pound  of 
the  substance  in  question,  by  the  process  of  combustion.  The  heat  of 
formation  of  the  common  products  of  combustion  will  be  found  in  Table 
XIII,  together  with  their  specific  heats  (or  water  equivalents  per  pound). 

TABLE  XIII 
PROPERTIES   OF  THE   CONSTITUENTS   OF   FLUE    GASES 


Name  of  Substance. 

Symbol. 

Heat  of 
Formation. 

Weight  of  O  in 
One  Pound. 

Specific  Heat 
at  Constant 
Pressure. 

Carbon  monoxide  
Carbon  dioxide 

CO 
CO, 

1845 
3950 

0.571 
0.727 

0.243 

0.189 

Water                                 

H,O 

6890 

0.890 

0.461 

Sulphur  dioxide       

SO2 

2010 

0.499 

0.154 

Phosphorus  pentoxide  
Oxygen            

PA 

O2 

4520 

0  .  563 

0.217 

Nitrogen 

N, 

0.244 

Air                            

0.237 

224.  The  Combustion  of  Carbon.  The  simplest  case  of  combustion 
is  that  of  pure  carbon.  When  incandescent  carbon  in  small  lumps  is 
placed  in  a  draft  of  air,  the  carbon  unites  with  the  oxygen  of  the  air 
to  form  carbon  dioxide  and  carbon  monoxide.  If  the  temperature  is 
high  and  the  air  supply  is  scanty,  large  quantities  of  CO  will  be  formed. 
If  the  gases  of  combustion  are  subsequently  brought  into  contact  with 
air  while  sufficiently  hot,  the  CO  will  burn  to  CO2,  evolving  a  large  amount 
of  heat.  If,  however,  the  gases  of  combustion  are  permitted  to  cool 
before  bringing  them  in  contact  with  the  air,  the  CO  will  not  burn. 

Dry  air  consists  of  20.7  per  cent  by  volume  of  oxygen,  and  79.3  per 
cent  by  volume  of  nitrogen  and  other  inert  gases.  The  inert  gases  will 
be  termed  nitrogen  in  this  discussion.  By  weight  air  consists  of  23  per 


ART.  225  THE  COMBUSTION  OF  CARBON  IN  AIR  217 

cent  of  oxygen  and  77  per  cent  nitrogen.      When  a  pound  of  carbon  is 
burned  to  CO2  in  air,  we  have  for  the  formula  of  the  reaction. 


=  C02. 
12     32      44 

Underneath  the  chemical  symbols  are  written  the  molecular  weights  of 
the  substances.  These  indicate  that  12  pounds  of  carbon  'unite  with  32 
pounds  of  oxygen  to  form  44  pounds  of  carbon  dioxide.  By  simple 
proportion  it  will  be  seen  that  1  pound  of  carbon  unites  with  2.67  pounds 
of  oxygen  to  form  3.67  pounds  of  carbon  dioxide.  Since  air  contains 
23  per  cent  of  oxygen  by  weight,  it  requires  11.6  pounds  of  air  to  supply 
this  2.67  pounds  of  oxygen.  If,  however,  we  attempt  to  burn  a  pound  of 
carbon  with  just  sufficient  air  to  complete  the  combustion,  we  will  find 
that  some  carbon  monoxide  will  be  formed  and  some  of  the  oxygen  will 
fail  to  combine,  and  that  it  is  necessary  to  supply  an  excess  of  air  in 
order  to  insure  the  complete  combustion  of  the  carbon  and  obtain  its 
full  heating  value. 

225.  The  Combustion  of  Carbon  in  Air.  It  may  be  shown,  however,1 
that  the  economical  use  of  fuel  requires  that  the  amount  of  the  excess 
air  be  made  as  small  as  possible.  Iri  practice  it  is  found  that  the  fuel 
is  utilized  to  the  best  advantage  when  from  30  to  50  per  cent  excess  of 
air  is  supplied.  Assume  that  15  pounds  of  air  are  used  to  burn  1  pound  of 
carbon.  In  this  15  pounds  of  air  are  3.45  pounds  of  oxygen  and  11.56 
pounds  of  nitrogen.  As  a  result  of  the  combustion  2|  pounds  of  the  oxygen 
unite  with  1  pound  of  carbon  to  form  3f  pounds  of  CO2  and  0.78  pounds 
of  oxygen  remain  in  the  free  state,  as  does  also  the  11.55  pounds  of  nitro- 
gen. The  products  of  combustion  are  usually  termed  flue  gas.  Since 
the  volume  of  the  carbon  dioxide  is  the  same  as  the  volume  of  the  oxy- 
;  gen  from  which  it  was  formed,  the  volume  of  the  16  pounds  of  flue  gas 
is  the  same  as  the  volume  of  the  16  pounds  of  air  at  the  same  temperature. 

The  heat  generated  by  the  above  combustion  will  be  found  by  careful 
calorimeter  measurements  to  be  14,500.  B.T.U.  The  water  equivalent  of  the 
products  of  combustion  is  found  by  multiplying  the  weight  of  each  con- 
stituent by  its  specific  heat  at  constant  pressure  (since  the  combustion 
occurs  at  constant  pressure),  and  adding  the  products.  The  water 
equivalent  of  the  CO2  is  3.67X0.217;  of  the  oxygen,  0.78X0.217;  of 
the  nitrogen,  11.55X0.244.  Adding  the  products,  it  will  be  found  that 
the  water  equivalent  of  the  16  pounds  of  gas  is  3.792.  A  quantity  of 
very  great  importance  in  the  theory  of  fuel  economy  js  the  theoretical 
temperature  of  the  fire,  which  is  found  by  adding  to  the  initial  tempera- 
ture of  the  air  and  fuel  which  may  be  taken  as  the  temperature  of  the 

1  See  Arts."  246  and  248. 


218  COMBUSTION  ART.  226 

fire  room,  the  rise  in  temperature  theoretically  produced  by  the  heat  of 
combustion.  Dividing  the  heat  of  combustion  by  the  water  equivalent 
of  the  flue  gases,  we  have  for  the  theoretical  rise  in  temperature  due  to 
the  combustion,  3830°  F.,  and  assuming  that  the  original  temperature 
of  the  air  and  the  carbon  was  70°,  we  have  for  the  theoretical  temperature 
of  the  fire  3900°  F.1 

226.  The  Combustion  of  Hydrogen.     The   combustion   of   hydrogen 
is  a  reaction  represented  by  the  formula  : 


2X2     32     2X18 

From  the  molecular  weights  it  will  be  seen  that  1  pound  of  hydrogen 
requires  8  pounds  of  oxygen  for  its  combustion,  the  result  being  9  pounds  of 
water  vapor.  Assuming  that  50  per  cent  excess  of  air  is  used,  it  will  be  seen 
that  this  air  must  contain  12  pounds  of  oxygen  and  that  the  total  quantity 
of  air  will  be  ,52.2  pounds.  The  heat  of  combustion  will  be  62,032  B.T.U 

The  products  of  combustion  will,  of  course,  be  9  pounds  of  water,  4 
pounds  of  oxygen,  and  42.2  pounds  of  nitrogen.  The  water  equivalent 
of  these  products  of  combustion  will  be  15.00.  In  reducing  the  products 
of  combustion  from  the  temperature  of  the  fire  to  their  original  tempera- 
ture, the  steam  formed  will  be  reduced  to  water.  The  latent  heat  of 
evaporation  of  this  steam,  which  will  be  9  X  1051.5=  13,640  B.T.U.  at  70° 
F.,  will  be  liberated  by  this  condensation.  Since  this  heat  is  latent,  it 
has  no  effect  in  raising  the  temperature  of  the  products  of  combustion. 
Hence,  the  heat  available  for  producing  the  rise  in  temperature  is  63,032 
-  13,640  =  49,392  B.T.U.  This  quantity  is  sometimes  known  as  the  lesser 
heat  of  combustion  of  hydrogen.  Dividing  this  quantity  by  the  water 
equivalent,  we  have  for  the  theoretical  rise  in  temperature  3290°  and  for 
the  theoretical  temperature  of  the  furnace  3360°. 

1  In  practice,  the  temperature  of  the  fire,  when  1  pound  of  carbon  is  burned  by 
15  pounds  of  air,  is  very  much  less  than  the  figure  given,  for  several  reasons.  In  the 
first  place,  the  fire  radiates  heat  into  the  boiler  and  the  walls  of  the  furnace,  and  the 
heat  available  for  producing  the  rise  in  temperature  is  diminished  by  the  amount  so 
radiated.  In  the  second  place,  when  the  temperature  has  risen  to  between  3000  and  3200° 
F.,  carbon  monoxide  is  formed  instead  of  carbon  dioxide,  and  the  quantity  of  heat 
evolved  is  less  than  14,500  B.T.U.  per  pound  of  carbon.  This  carbon  monoxide,  if  mixed 
with  sufficient  air,  will  of  course  burn  to  carbon  dioxide  as  soon  as  the  temperature 
falls  sufficiently.  This  phenomenon  is  known  as  suppressed  combustion.  In  the 
third  place,  it  is  found  that  the  specific  heat  of  a  gas  increases  with  the  temperature  , 
so  that  even  if  complete  combustion  did  occur,  and  no  heat  was  radiated,  the  temperature 
realized  would  not  be  the  theoretical  temperature  obtained  by  assuming  a  constant 
specific  heat.  However,  so  long  as  the  actual  temperature  of  the  furnace  is  sufficiently 
great  to  maintain  rapid  combustion,  it  is  of  no  practical  importance  what  the  actual 
temperature  is.  On  the  other  hand,  the  theoretical  temperature  of  the  fire  is  of  the 
greatest  importance,  since  it  determines  the  efficiency  of  the  boiler  plant. 


ART.  227         THE  COMBUSTION  OF  CHEMICAL  COMPOUNDS  219 

227.  The  Combustion  of  Chemical  Compounds.  When  a  compound 
of  carbon  and  hydrogen  is  burned,  the  carbon  burns  to  carbon  dioxide 
and  the  hydrogen  to  water.  In  estimating  the  quantity  of  oxygen  required, 
we  must  first  find  the  weight  of  carbon  and  of  hydrogen  in  1  pound  of 
the  substance  and  allow  sufficient  oxygen  to  burn  both  the  carbon  and 
the  hydrogen.  The  weight  of  the  products  of  combustion  can  be  com- 
puted from  the  weight  of  carbon  and  hydrogen  present  in  a  pound  of 
the  substance.  The  theoretical  rise  in  temperature  may  be  computed 
by  subtracting  from  the  heat  of  combustion  the  latent  heat  of  evapora- 
tion at  atmospheric  temperature  of  the  water  formed  by  the  combustion, 
and  dividing  the  difference  by  the  water  equivalent  of  the  products  of 
combustion. 

Some  fuels,  as  for  instance  wood,  which  consists  largely  of  a  chemical 
substance  termed  cellulose,  contain  oxygen  as  well  as  carbon  and  hydrogen. 
The  chemical  reaction  resulting  from  the  combustion  of  cellulose  may  be 

written  C6H10O5+  6  O2  =  6  CO2  +  5  H2O. 

162          6X32     6X44        5x18 

From  this  it  will  be  seen  that  1  pound  of  cellulose  consists  of  .444 
pounds  of  carbon,  0.0618  pounds  of  hydrogen,  and  0.494  pounds  of  oxygen. 
The  oxygen  is,  of  course,  not  a  combustible,  and  the  hydrogen  is  already 
united  with  the  oxygen  in  the  compound,  and  hence  is  not  available 
as  a  combustible.  The  only  combustible  present  is  the  .414  pounds  of 
carbon  whose  combustion  will,  in  theory,  yield  6240  B.T.U.  In  any 
chemical  compound  containing  oxygen,  the  oxygen  is  united  with  one  of 
the  combustible  elements,  and  the  heat  of  combustion  is  usually  approxi- 
mately equal  to  that  of  the  combustible  substances  not  united  with  oxygen 
present  in  1  pound  of  the  compound. 

It  may  be  noted  that  the  heat  of  combustion  of  a  compound  may  be 
more  or  less  than  the  heat  of  combustion  of  the  elements  forming  it. 
For  instance,  the  heat  of  combustion  of  acetylene  is  found  to  be  21,429 
B.T.U.  One  pound  of  acetylene  consists  of  12/i3  of  a  pound  of  carbon 
and  V13  of  a  pound  of  hydrogen.  The  heat  of  combustion  of  the  carbon 
will  be  12A3X  14,500  =13,400  B.T.U.,  and  of  the  hydrogen  63, 032  X  Via  = 
4850  B.T.U.  The  sum  of  these,  or  18,250  B.T.U.,  is  less  than  the  heat  of 
combustion  of  acetylene.  A  chemical  compound  must  be  decomposed 
before  it  can  be  burned.  The  decomposition  of  the  compound  absorbs 
heat  in  many  cases,  for  instance  in  the  case  of  marsh-gas.  Such  a  com- 
pound is  termed  endothermic.  In  other  cases,  acetylene  for  instance,  heat 
is  given  up  as  a  result  of  the  decomposition.  Such  a  compound  is  termed 
exothermic.  The  heat  of  combustion  of  exothermic  substances  is  more, 
and  of  endothermic  substances  less,  than  the  heat  of  combustion  of  their 
chemical  constituents. 


220 


COMBUSTION 


ART.  228 


228.  Flue  Gas  Analysis  by  the  Or  sat  Apparatus.  •  In  engineering 
work  computations  relative  to  the  efficiency  of  combustion  must  usually 
be  based  upon  the  results  of  a  chemical  analysis  of  the  flue  gases.  Flue 
gases  are  usually  analyzed  by  means  of  the  Orsat  apparatus,  which  deter- 
mines the  volume  of  CO2,  of  O2,  and  of  CO  present  in  a  sample  of  dry  gas. 
The  remainder  of  the  gas  is  nitrogen  and  other  inert  elements.  The  form 
of  the  Orsat  apparatus  is  shown  in  Fig.  116.  The  gas  to  be  analyzed 
is  drawn  into  the  measuring  burette  A  by  manipulating  the  water  bottle 

B.  The  measuring  burette  holds  exactly   100  c.c.  of  gas.     By  manip- 
ulating the  water  bottle,  this  gas  is  first  passed  into  the  treating  pipette 

C,  containing  a  solution  of  potassium  hydroxide,  which  absorbs  the  CO2. 
After  being  passed  several  times  into  pipette  C,  the  gas  is  withdrawn  arid 
measured  in  the  burette  A.     The  shrinkage  in  volume  indicates  the  per 
cent  by  volume  of  CO2.     In  like  manner,  the  gas  is  introduced  into  the 
pipette  D  containing  a  solution  of  potassium  pyrogallate,  which  absorbs 
the  oxygen,  and  then  into  pipette  E  containing  an  acidulated  solution 
of  cuprous  chloride,  which  absorbs  the  carbon  monoxide.     The  shrinkage 
in  volume  in  each  case  indicates  the  per  cent  by  volume  which  the  gas 
removed  bears  to  the  whole  quantity  taken.     Since  the  gas  is  in  contact 
with  water  while  it  is  being  measured,  and  the  apparatus  is  kept  at  con- 
stant temperature,  the  gas  is  always  saturated  with  water  vapor,  and 
the  pressure  of  the  water  vapor  is  constant.     Consequently,  when  the 
volume  of  the  gas  in  the  apparatus  is  reduced 

by  absorbing  a  given  proportion  of  it,  the  same 
proportion  of  the  total  quantity  of  the  water 
vapor  present  is  condensed,  and  although  the 
gas  comes  from  the  stack  loaded  with  moisture 
and  is  analyzed  while  it  contains  this  moisture, 
the  results  given  by  the  apparatus  are  those 
which  would  be  obtained  by  analyzing  a 
sample  of  the  gas  after  the  moisture  has  been 
abstracted. 

When  a  substance  containing  hydrogen  is 
burned,  and  the  flue  gases  analyzed  by  the 
Orsat  apparatus,  it  will  be  found  that  the 
volume  of  the  oxygen  accounted  for  by  the 
analysis  will  be  less  than  26.1  percent  of  the 
volume  of  the  nitrogen . 1  The  per  cent  of  oxygen 
accounted  for  by  the  analysis  is  equal  to  the  FIG.  116.— Orsat  apparatus, 
per  cent  of  CO2  plus  the  per  cent  of  O2  plus 
one-half  the  per  cent  of  CO  shown  by  the  analysis,  since  each  volume 

1  Since  air  consists  of  20.7  per  cent  O2  and  79.3  per  cent  nitrogen,  each  volume  of 
atmospheric  nitrogen  will  be  mixed  with  26.1  per  cent  of  its  volume  of  O2. 


ART.  229  EFFICIENCY  OF  COMBUSTION  221 

of  CO2  requires  one  volume  of  O2  and  each  volume  of  CO  one-half  a  volume 
of  O2  for  its  formation. 

229.  Computations  of  the  Efficiency  of  Combustion  Based  on  a  Volu- 
metric Analysis  of  the  Flue  Gases.  Let  N  equal  the  number  of  cubic 
centimeters  of  nitrogen,  0  the  number  of  cubic  centimeters  of  free 
oxygen,  Coo  the  number  of  cubic  centimeters  of  carbon  dioxide,  and  Co 
the  number  of  cubic  centimeters  of  carbon  monoxide  in  each  100  c.c. 
of  dry  flue  gas,  as  shown  by  the  flue  gas  analysis.  Then,  for  the  num- 
ber of  cubic  centimeters  of  oxygen  accounted  for  in  100  c.c.  of  flue  gas,  we 
will  have 

(0+  Coo+~)c.c.       .    .;     .....     (1) 

The  oxygen  represented  by  the  nitrogen  in  100  c.c.  of  flue  gas  will  be 

0.261  TV  c.c  ..........     (2) 

The  difference  will  give  the  number  of  cubic  centimeters  of  oxygen 
represented  by  the  nitrogen  in  100  c.c.  of  flue  gas  which  combined  with 
hydrogen  to  form  water  vapor.  This  will  be 


0.261  N-o  +  Coo+-=Ac.c  ......     .     (3) 

Assume  for  a  unit  of  mass  1  c.c.  of  a  gas  whose  molecular  weight  is  1. 
Then  the  weight  of  the  carbon  in  1  c.c.  of  CO2  or  CO  will  be  12,  since 
the  atomic  weight  of  carbon  is  12,  and  the  weight  of  the  carbon  in  100 
c.c.  of  flue  gas  will  be 

(Coo  +  Co)  12. 

The  number  of  cubic  centimeters  of  oxygen  accounted  for  in  100  c.c.  of 
flue  gas  is  .261  N.  The  weight  of  1  c.c.  of  oxygen  will  be  32.  Consequently 
the  weight  of  oxygen  accounted  for  in  100  c.c.  of  flue  gas  will  be 

0.261  7VX32. 

The  number  of  pounds  of  carbon  burned  by  each  pound  of  oxygen  sup- 
plied will  therefore  be 

(Coo  +  Co)  12 

0.261  NX32 

reducing,  this  becomes 

1.44  (Coo  +  Co)  u 

c=         ~     lbs  ........ 


222  COMBUSTION  ART.  229 

In  like  manner  it  may  be  shown  that  the  number  of  pounds  of  hydrogen 
burned  per  pound  of  oxygen  supplied  will  be 


The  excess  of  air  supplied  will  be 

3830 


of  that  theoretically  necessary. 

Adding  C  from  (4)  ,  and  H  from  (5)  ,  we  will  have  the  number  of  pounds 
of  combustible  per  pound  of  oxygen  supplied.  For  the  number  of  pounds 
of  air  supplied  per  pound  of  combustible  we  will  have 

.........     (7) 


C+H- 


For  the  number  of  pounds  of  nitrogen  in  the  flue  gas  per  pound  of  com- 
bustible, we  will  have 

3.35 


C  +  H' 

For  the  number  of  pounds  of  carbon  dioxide  in  the  flue  gas  per  pound 
of  combustible  we  will  have 

5.27  Coo  . 

Ibs (9) 


For  the  number  of  pounds  of  carbon  monoxide  in  the  flue  gas  per  pound 
of  combustible,  we  will  have 

3.36  Co 

11 


For  the  number  of  pounds  of  water  vapor  in  the  flue  gas  per  pound  of 
combustible,  we  will  have 

4.20  A 

Ibs (11) 


For  the  number  of  pounds  of  free  oxygen  in  the  flue  gas  per  pound  of 
combustible,  we  will  have 

3.83  O 


(C  +  H) 


Ibs (12) 


ART.  230  THE  COMPOSITION  OF  COAL  223 

The  heat  evolved  per  pound  of  combustible  will  be 
6340  Co  +  20900  Coo +  29400  A 


(C+H) 


B.T.U.     .     .     .     .     (13) 


Dividing  this  by  the  water  equivalent,  which  may  be  readily  obtained 
from  the  weights  of  the  various  constituents  of  the  flue  gas  per  pound  of 
combustible,. we  will  obtain  the  theoretical  rise  in  temperature.  Adding 
the  air  temperature,  we  will  obtain  the  theoretical  fire  temperature.  For 
an  example  of  the  application  of  the  theory  of  combustion  to  an  actual 
boiler  test  the  reader  is  referred  to  Art.  252. 

230.  The  Composition  of  Coal.     The  fuel  of  greatest  practical  value 
in  engineering  work  is  coal.     Coal  is  fossil  vegetable  matter  which  under 
the  combined  influence  of  heat  and  pressure  has  been  changed  materially 
in  its  chemical  and  physical  form.     It  consists  of  carbon  and  hydro- 
carbon compounds,  together  with  varying  amounts  of  water  and  ash. 
The  moisture,  which  varies  from  0.25  to  8.0  per  cent  by  weight  of  the 
coal,  may  be  driven  off  by  heating  it  to  a  temperature  of  220°  F.  for  an 
hour  or  more.     If  the  coal  be  heated  to  a  red  heat,  and  the  air  is  excluded 
during  the  process,  the  hydro-carbons  will  be  driven  off,  and  carbon  and 
ash  will  remain  behind.     The  hydro-carbons  so  driven  off  are  termed 
volatile  matter.     The  substance  remaining  is  termed  coke,  and  the  carbon 
of  the  coke  is  termed  fixed  carbon.     If  coke  is  heated  in  the  presence  of 
the  air,  for  a  sufficient  length  of  time  it   will  burn,  leaving  behind  the 
ash,  which  usually  consists  of  sand,  clay,  iron  oxide,  lime,  etc.     When  the 
moisture,  volatile  matter,  fixed  carbon,  and  ash  are  determined,  the  proc- 
ess is  termed  proximate  analysis. 

Coal  is  classified  as  bituminous,  semi-bituminous  and  anthracite,  accord- 
ing as  it  contains  more  or  less  volatile  matter.  Bituminous  coals  are  coals 
containing  from  20  to  50  per  cent  of  volatile  matter.  They  may  be  divided 
into  coking  and  non-coking  coals.  If  the  volatile  matter  of  a  coal  will 
melt  before  vaporizing  the  coal  is  said  to  coke,  or  cake,  since  it  will  be 
fused  into  a  compact  mass  of  coke  while  burning.  If,  on  the  other  hand, 
the  volatile  matter  vaporizes  without  melting,  the  coal  is  termed  non- 
coking  coal.  Semi-bituminous  coals  are  those  containing  from  12  to  20 
per  cent  of  volatile  matter.  Anthracite  coals  are  those  containing  less 
than  12  per  cent  of  volatile  matter.  The  volatile  matter  of  coal  consists 
mostly  of  hydro-carbon  compounds  which  may,  and  in  the  case  of  bitu- 
minous coals  high  in  volatile  matter,  usually  do  contain  some  oxygen. 

231.  The  Heating  Value  of  Coal.     The  heating  value  of  coal  varies 
greatly,   as  may  be  inferred  from  the  great  variation  in  composition. 
The  moisture  and  ash,  of  course,  have  no  heating  value.     The  oxygen 
contained  in  the  hydrogen  compounds  also  h:s  no  heating  value,  and 


224 


COMBUSTION 


AKT.  232 


furthermore,  since  it  is  already  combined  with  a  portion  of  the  hydrogen 
of  these  compounds,  it  reduces  the  heating  value  of  the  combustible 
elements  present.  The  heating  value  of  the  coal  may  be  obtained  approx- 
imately from  the  formula* 

H~}  +4,100  S, 
o 


B.T.U.  =  14,5000  +  63  ,000 


in  which  C  is  the  number  of  pounds  of  carbon,  H  is  the  number  of  pounds 
of  hydrogen,  and  S  is  the  number  of  pounds  of  sulphur  per  pound  of 
coal,  as  obtained  from  the  ultimate  chemical  analysis. 

A  more  exact  result  for  the  heating  value  may  be  obtained  by  the 
use  of  a  calorimeter.  The  form  of  calorimeter  invented  by  Parr  is  espe- 
cially suitable  for  engineering  use  and  gives  dependable  results  when 
calibrated  by  burning  in  it  chemically  pure  sugar  of  known  heating  value. 


15,000 


o    14,000 


13,000 


12,000 


.10 


.20 


.30  .40  .50  .60  .70 

llatio  of  Volatile  Matter  to  fixed  Carbon. 


-80 


.90 


.100 


FIG.  117.  —  The  heating  value  of  coal. 

The  heating  value  of  coal  may  also  be  determined  with  considerable 
accuracy  from  the  proximate  analysis  as  follows  :  Deduct  the  percentage 
of  moisture  and  ash  as  shown  by  the  proximate  analysis,  the  result  will 
be  the  percentage  of  combustible  in  the  coal.  Divide  the  per  cent  of 
volatile  matter  by  the  per  cent  of  fixed  carbon.  From  the  curve  in  Fig. 
117,  obtain  the  heating  value  per  pound  of  combustible,  of  coal  having 
this  ratio  of  volatile  matter  to  fixed  carbon.  Multiplying  this  value  by 
the  per  cent  of  combustible  in  the  coal  will  give  the  heating  value  of  the 
coal  in  B.T.U.  per  pound. 

232.  The  Combustion  of  Coal.  Coal  is  burned  on  a  grate  whose  pur- 
pose it  is  to  admit  air  to  the  under  side  of  the  fire  and  to  permit  of  the 
removal  of  ash  from  the  fire.  (1  rates  are  of  various  forms  and  are  arranged 
in  various  ways  in  order  to  adapt  them  to  different  kinds  of  coal  and 
conditions  of  service.  The  simplest  grate  consists  of  parallel  bars  of  cast 


ART.  233  THE  PRODUCTION  OF  SMOKE  225 

iron  upon  which  the  fire  is  laid.  Assuming  such  a  grate,  with  a  fire 
built  upon  it,  we  may  note  the  following  phenomena  with  respect  to  the 
combustion  of  coal : 

Pure  carbon  burns  without  flame  to  carbon  dioxide.  In  the  presence 
of  an  excess  of  carbon,  this  carbon  dioxide  is  decomposed,  forming  carbon 
monoxide,  which  burns  with  a  flame.  A  fire  of  pure  carbon,  or  coke, 
of  moderate  depth  will  therefore  burn  with  little  or  no  flame.  In  order 
to  utilize  the  fuel  as  economically  as  possible,  it  is  necessary,  as  has  already 
been  noted,  to  burn  the  carbon  with  the  least  possible  excess  of  air. 
The  excess  of  air  will  be  determined  by  the  intensity  of  the  draft  and  the 
thickness  of  the  fire,  consequently  it  is  necessary  to  so  adjust  the  thick- 
ness of  the  fire  that  the  quantity  of  air  will  be  the  minimum  necessary 
to  maintain  the  required  rate  of  combustion.  If  the  quantity  of  air 
admitted  to  the  under  side  of  the  fire  be  less  than  that  required  for  com- 
-plete  combustion,  some  air  must  be  admitted  at  the  top  of  the  fire,  in 
order  to  burn  the  carbon  monoxide  which  will  be  formed.  It  is  usual 
in  practice  to  carry  the  fire  slightly  thicker  than  is  necessary  and  then  to 
admit  a  proper  quantity  of  air  over  the  fire  in  order  to  secure  complete 
combustion. 

233.  The  Production  of  Smoke.  If  upon  such  a  coke  fire  a  layer  of 
bituminous  coal  is  spread,  the  water  and  volatile  matter  in  the  coal  will 
be  quickly  vaporized  by  the  heat.  A  considerable  proportion  of  this 
volatile  matter  is  tar.  Tar  vapor  is  difficult  to  burn,  since  its  kindling 
temperature  is  high,  and  the  rate  of  combustion,  on  account  of  the  com- 
paratively great  density  of  the  vapor,  is  much  lower  than  is  the  case  with 
other  combustible  gases.  As  the  tarry  vapors  rise  from  the  coal,  they 
are  mingled  with  the  products  of  combustion  and  with  an  excess  of  free 
oxygen.  If  the  temperature  of  the  mass  is  above  the  kindling  point  of 
the  tar  vapor,  and  it  remains  at  this  temperature  for  a  sufficient  length 
of  time  to  permit  of  a  complete  mixture  of  the  various  gases,  the  tar  will 
be  burned  to  water  and  carbon  dioxide.  If,  however,  the  vapor  is 
cooled  below  its  kindling  point  before  it  has  an  opportunity  to  completely 
mix  with  the  air,  it  will  not  become  ignited,  but  will  be  discharged  from 
the  chimney  in  the  form  of  unburned  vapor.  As  soon  as  the  temperature 
of  the  chimney  gas  becomes  low  enough  to  permit  of  the  liquefaction  of 
these  unburned  vapors,  they  are  condensed  upon  particles  of  dust  and 
form  specks  of  soot,  which  give  to  the  gases  coming  from  the  chimney 
the  intensely  black  appearance  which  we  note  in  soft  coal  smoke. 

The  amount  of  potential  heat  carried  away  in-  the  flue  gases  as  a 
result  of  such  incomplete  combustion  is  usually  comparatively  small, 
often  being  less  than  two  per  cent  of  the  total  heat  o£  the  coal,  when  the 
smoke  is  very  dense  and  black.  Most  of  the  volatile  matter  is  burned 
in  the  furnace,  and  only  a  small  portion  of  it  escapes  combustion  and 


226 


COMBUSTION 


ART.  233 


produces  the  smoke.  However,  the  pollution  of  the  air  of  our  cities  by 
vast  quantities  of  black  smoke  is  highly  objectionable  for  many  reasons. 
Hence  many  attempts  have  been  made  to  compel  owners  of  steam  plants 
to  so  construct  and  operate  their  furnaces  as  to  avoid  the  production  of 
smoke.  It  will  be  apparent  that  there  are  two  possible  methods  of  pre- 
venting the  escape  of  smoke  from  a  chimney.  The  first  one  is  to  cool  the 
products  of  combustion  and  mechanically  extract  the  dust  and  tar  from 
them.  This  method  is  commercially  impracticable,  although  it  has  been 
seriously  proposed  as  a  remedy  for  the  smoke  nuisance.  The  second 
method  consists  in  thoroughly  mixing  the  vapors  coming  from  the  fire 


FIG.  118. — Horizontal  return  tubular  boiler  equipped  with  a  Dutch  oven  furnace. 


with  a  sufficient  quantity  of  highly  heated  air  before  they  have  been 
cooled  below  their  kindling  point. 

When  a  combustible  gas  or  vapor  is  intimately  mixed  by  diffusion 
with  an  excess  of  highly  heated  air,  combustion  is  very  rapid,  only  a 
fraction  of  a  second  being  necessary  to  practically  complete  the  reaction. 
However,  in  the  case  of  a  coal  fire,  hand  fed  in  the  ordinary  manner,  the 
gases  are  not  thoroughly  mixed  as  they  rise  from  the  fire,  since  the  ari 
tends  to  pass  through  the  holes  of  the  fire,  and  the  volatile  matter  of  the 
coal  is  separated  from  the  surrounding  air  by  the  products  of  combustion. 
Columns  of  air  arise  from  some  portions,  and  columns  of  combustible 
vapors  from  other  portions,  of  such  a  fire.  These  tend  to  pass  through 
the  furnace  in  parallel  streams,  diffusion  and  combustion  occurring  only 
at  the  boundaries  of  the  streams.  As  soon  as  the  streams  of  gas  encounter 


ART.  233 


THE  PRODUCTION  OF  SMOKE 


227 


FIG.  119. — Furnace  equipped  with  tile  roof  attached  to  lower  row  of  boiler  tubes. 


FIG.  120.^— Kent  wing-wall  furnace 


228  COMBUSTION  ART.  234 

a  cold  metallic  surface  they  are  cooled  below  their  kindling  point,  com- 
bustion ceases,  and  smoke  is  produced. 

234.  Methods  of  Smoke  Prevention.     Three  general  methods  are  in 
use  for  securing  a  thorough  mixing  of  the  combustible  vapors  with  heated 
air  before  they  are  cooled.     The  first  of  these  methods  consists  in  leading 
the  combustible  gases  and  the  air  coming  from  the  fire  into  a  chamber 
of  sufficient  size,  so  that  they  may  remain  in  it  long  enough  to  be  thoroughly 
mixed.     In  order  that  the  temperature  of  this  chamber  may  be  above  the 
kindling  point  of  the  gases,  it  is  lined  with  fire  brick,  which  soon  becomes 
incandescent.     In  order  to  make  the  process  of  mixing  quicker  and  more 
thorough  this  chamber  is  sometimes  so  arranged  that  the  currents  of  gas 
and  air  are  baffled  in  their  progress  and  made  to  mix  as  a  result  of  the 
eddying  produced  by  the  baffles. 

235.  The  Dutch  Oven.      The  Dutch  oven  furnace  illustrated  in  Fig. 
118  is  an  example  of  a  combustion  chamber  of  incandescent  fire  brick 
in  which  the  gases  are  permitted  to  mix.     It  consists  of  a  large  chamber 
over  the  fire  with  walls  and  roof  of  fire  brick.     If  the  condition  of  the 
fire  is  kept  uniform  by  careful  firing,  the  gases  will  be  quickly  and  thor- 
oughly mixed  in  this  chamber  and  combustion  will  be  complete.     The 
same  result  is  accomplished  by  the  furnace  shown  in  Fig.  119,  in  which 
the  roof  of  the  furnace  is  not  a  brick  arch,  but  consists  of  tiles  of  fire  clay 
attached  to  the  lower  row  of  tubes  of  the  boiler.     The  Kent  wing-wall 
furnace  illustrated   in  Fig.  120  is  an  example  of  a  furnace  in  which  the 
gases  are  caused  to  mingle  by  means  of  baffles.     As  the  gases  pass  from 
the  Dutch  oven  over  the  bridge  wall  7),  they  strike  against  the  wing  walls 
E}  whose  purpose  it  is  to  cause  the  streams  of  gas  to  mingle  as  a  result 
of  the  eddy  currents  which  they  create. 

236.  The  Mechanical  Stoker.     The  second  method  of  securing  smoke- 
less combustion  consists  in    introducing   the  coal  continuously  into  the 
furnace  and  in  so  directing  the  gases  rising  from  the  fire  that  they  shall 
be  caused  to  mingle.     The  chain-grate  stoker  and  the  rocking-grate  stoker 
are   examples    of    this   method    of    securing   smokeless    combustion.     A. 
chain-grate  stoker  is  illustrated  in  Fig.  121.     Coal  is  fed  into  the  hopper 
and  the  grate  consists  of  a  series  of  parallel  bars  attached  at  either  end  to 
a   chain.     The  motion   of   the   chains,  which   are   operated   by  gearing, 
carries  the  coal  bodily  into  the  fire.     A  rocking-grate  stoker  is  shown  in 
Fig.   122.     The  coal  passes  from  the  hopper  on  to  the  grate,  which  is 
inclined,  and  the  rocking  motion  of  the  grate  causes  it  to  slide  down, 
burning  as  it  goes.     The  chain-grate  stoker  is  particularly  adapted  to  the 
use  of  anthracite  coal  and  non-coking  coals.      The  rocking-grate  stoker 
is  particularly  adapted  to  the  use  of  coking  coals. 

Since  coal  is  introduced  continuously  into  the  fire  when  a  stoker -is 
used;  and  large  quantities  of  volatile  matter  are  not  given  off  at  once, 


ART.  237 


THE  DOWN-DRAFT  FURNACE 


229 


as  is  usually  the  case  with  poor  hand  firing,  the  gases  have  a  much  better 
opportunity  to  mix  with  a  sufficient  quantity  of  heated  air,  and  combustion 
will  accordingly  be  more  complete.  A  chain  grate  or  rocking  grate  stoker, 
however,  will  not  give  absolutely  smokeless  combustion  unless  a  fire- 
brick combustion  chamber  of  one  of  the  types  described  in  Art.  235  is 
used  in  connection  with  it. 

237.  The  Down- draft  Furnace.  The  third  method  of  securing  smoke- 
less combustion  consists  in  passing  the  combustible  gases  through  the 
fire.  This  is  accomplished  either  by  drawing  the  air  and  products  of 
combustion  downward  through  the  fire,  or  by  introducing  the  fresh  coal 


FIG.  121.— Chain  grate  stoker. 

at  the  bottom  of  the  fire.  The  first  of  these  methods  is  the  one  employed 
in  the  Hawley  Down-draft  furnace  illustrated  in  Fig.  123.  The  fire  is 
built  upon  the  upper  grates,  which  are  iron  tubes  filled  with  water  from 
the  boiler.  The  fresh  coal  is  spread  on  top  of  the  fire  and  the  air  passes 
downward  through  the  fire.  The  temperature  of  the  incandescent  coke 
through  which  the  air  and  volatile  matter  passes  is  sufficient  to  decom- 
pose the  tarry  vapors,  and  insure  their  complete  combustion.  As  the 
coke  is  formed,  it  drops  through  onto  the  lower  grate,  where  it  is 
completely  burned 

The  under-feed  stoker  illustrated  in  Fig.  124  accomplishes  the  same 
result  by  the  second  method.     The  fresh  coal  is  introduced  at  the  bottom 


230 


COMBUSTION 


ART.  237 


FIG.  122.— Rocking-grate  stoker. 


FIG.  123. — Water  tube  boiler  equipped  with  Hawley  down-draft  furnace. 


ART.  238 


MANAGEMENT  OF  FIRES 


231 


of  the  fire  by  means  of  the  conveyor.  The  gases  distilled  from  it  pass 
upward  through  the  bed  of  incandescent  coke,  where  they  are  thoroughly 
mixed  with  highly  heated  air  and  burned.  A  stoker  of  this  type  gives 
absolutely  smokeless  combustion,  but  is  only  adapted  for  coals  which  have 
comparatively  little  ash  which  does  not  "  clinker." 

238.  The  Practical  Management  of  Fires.  Returning  to  a  considera- 
tion of  the  hand-fired  furnace  described  in  Art.  232,  it  may  be  noted  that 
the  ash  contained  in  the  coal  gathers  upon  the  grates  as  the  fire  burns 
and  must  be  removed  at  intervals  by  cleaning  the  fire,  i.e.,  by  separating 
the  ash  from  the  coke,  hoeing  out  the  ash,  and  then  spreading  the  coke 
again  over  the  grates.  Some  coals  contain  very  little  ash,  so  that  there 
is  no  difficulty  in  its  disposal.  Other  varieties  of  coal,  however,  contain 
large  amounts  of  ash,  and  sometimes  the  ash  is  of  such  a  character  that  it 
is  melted  by  the  heat  of  the  fire,  forming  masses  of  glass  termed  clinkers. 
Anthracite  coal  almost  invariably  produces  ash  which  clinkers  when  the 


FIG.  124. — Underfeed  stoker. 

fire  is  very  hot.  In  order  to  avoid  the  production  of  clinkers  with 
anthracite  coal,  it  is  customary  to  introduce  steam  into  the  ash  pit.  The 
steam  is  decomposed  by  the  carbon,  forming  hydrogen  and  carbon  mon- 
oxide. The  reaction  absorbs  heat  and  cools  the  under  side  of  the  fire 
below  the  melting  point  of  the  ash.  The  gases  formed  are  subsequently 
burned  when  they  reach  the  upper  side  of  the  fire,  and  they  there 
liberate  the  heat  which  they  absorb  from  the  lower  layer  of  fuel. 

When  the  fuel  used  is  a  coking  coal,  it  will  be  found  that  the  coal  fuses 
together  into  a  compact  mass  which  does  not  permit  of  the  passage  of 
air  through  the  fire.  In  order  to  allow  the  air  free  access  to  all  parts  of 
the  fire,  it  is  necessary  to  bar  or  slice  the  fire,  or  in  other  words,  to  break 
up  the  mass  of  coke  by  the  use  of  a  huge  poker.  The  finest  sizes  of  anthra- 
cite coal  are  in  certain  parts  of  the  country  a  very  cheap  fuel.  They  are 
difficult  to  burn,  however,  since  if  the  openings  in  the  grate  are  of  sufficient 
size  to  allow  a  proper  air  supply,  much  of  the  coal  will  fall  through.  In 
order  to  use  such  fuel,  it  may  be  mixed  with  a  coking  coal  in  the  propor- 


232  COMBUSTION  Probs.  1-12 

tion  of  three  parts  of  anthracite  to  one  of  bituminous  coal.  The  coking 
of  the  mixture  cements  the  anthracite  particles  together,  so  that  they  are 
much  more  readily  handled  in  the  furnace  and  the  loss  of  coal  through 
the  grates  is  very  much  reduced. 

The  proper  handling  of  a  coal  fire  is  a  matter  of  great  importance  in 
the  economical  operation  of  a  boiler  plant.  It  is  necessary  to  have  suffi- 
cient draft  to  operate  the  fire  at  the  required  rate  of  combustion.  The 
fire  must  be  kept  of  uniform  thickness  and  the  coal  must  be  spread  evenly 
upon  all  parts  of  it  unless  the  "  coking  method  "  of  firing  is  used.  If 
a  coking  coal  is  used,  the  fire  must  be  barred  as  soon  as  the  coke  is  formed. 
The  thickness  of  the  fire  must  be  adjusted  to  the  rate  of  combustion,  so 
that  the  least  possible  excess  of  air  is  used.  The  fire  doors  must  be  kept 
closed  as  much  as  possible,  since  when  they  are  open  large  volumes  of  cold 
air  will  be  drawn  into  the  furnace  and  heat  will  be  wasted  in  warming 
this  air  to  the  temperature  of  the  chimney  gas. 

In  the  coking  method  of  firing  the  fresh  coal  is  placed  at  the  very 
front  of  the  fire,  next  to  the  fire  doors.  As  soon  as  this  coal  is  coked,  it 
is  pushed  back  over  the  grates.  The  vapors  rising  from  it  while  it  is 
coking  pass  backward  over  the  bed  of  incandescent  coke  which  forms 
the  remainder  of  the  fire,  and  are  there  burned.  In  the  alternate  method 
of  firing,  first  one  side  and  then  the  other  is  covered  with  coal.  The  gases 
rising  from  the  fresh  coal  are  mingled  in  the  combustion  chamber  with 
the  excess  of  air  coming  from  the  other  side  of  the  fire,  and  there  burned. 

PROBLEMS 

1.  One  pound  of  carbon  is  burned  with  20  Ibs.  of  air.     Find  the  water  equivalent 
of  the  flue  gases.  Ans.     4.86. 

2.  Find  the  theoretical  rise  in  temperature.  Ans.     2980°. 

3.  One  pound  hydrogen  is  burned  with  80  Ibs.  of  air.    Find  the  water  equivalent 
of  the  flue  gases.  Ans.     20.4. 

4.  Find    the    theoretical    temperature    of    the    fire,    assuming    the    original    tem- 
perature to  be  100°.  Ans.    2680°  F. 

5.  One  pound  of  acetylene  is  burned  with  40  Ibs.  of  air.     Find  the  water  equivalent 
of  the  products  of  combustion.  Ans.     9.78. 

6.  Find  the  rise  in  temperature  resulting.  Ans.     2190°  F. 

7.  The  Orsat  analysis  of  a  flue  gas  shows  10  per  cent  of  CO2,  9  per  cent  of  Q2  and 
1  per  cent  of  CO2.     How  many  c.c.  of  oxygen  is  represented  by  the  nitrogen  in  100  c.c. 
of  flue  gas?  Ans.     20.9  c.c. 

8.  How  many  c.c.   of  this  oxygen  united  with  hydrogen?  Ans.      1.4  c.c. 

9.  How  many  pounds  of  carbon  were  burned  per  pound  of  oxygen  supplied? 

Ans.     0.198  Ibs. 

10.  How  many  pounds  of  hydrogen  were  burned  per,  pound  of  oxygen  supplied? 

Ans.     0.0084  Ibs. 

11.  What  per  cent  excess  of  air  was  supplied?  Ans.      75.8% 

12.  How  many  pounds  of  air  were  supplied  per  pound  of  combustible? 

Ans.     21.1  Ibs. 


PROBS.  13-20  PROBLEMS  233 

13.  How  many  pounds  of  carbon  monoxide  are  there  in  the  flue  gas  per  pound  of 
combustible?  Ans.     0.204  Ibs. 

14.  How  many  pounds  of  carbon  dioxide  are  there  in  the  flue  gas  per  pound  of 
combustible?  Ans.     3.20  Ibs. 

15.  How  many  pounds  of  water  vapor  are  there  in  the  flue  gas  per  pound  of 
combustible?  Ans.     0.356  Ibs. 

16.  How  many  pounds  of  free  oxygen  are  there  in  the  flue  gas  per  pound  of 
combustible?  Ans.     2.09  Ibs. 

17.  What  is  the  heat  evolved  per  pound  of  combustible?.       Ans.     15,550  B.T.U. 

18.  What    is  the  water    equivalent    of    the    products    of    combustion  per  pound 
combustible?  Ans.     5.23. 

19.  What  is  the  theoretical  fire  temperature,  assuming  the  initial  air  temperature 
to  be  70°.  Ans.    3050°  F. 

20.  A  coal  on  analysis  is  found  to  consist  of  4  per  cent  water,  10  per  cent  ash,  20 
per  cent  volatile  matter,  and  66  per  cent  fixed  carbon.     Find  its  heating  value. 

Ans.     13,600  B.T.U. 


CHAPTER  XV 


THE  STEAM   BOILER 

239.  The  Horizontal    Return    Tubular    Boiler.     The  steam  boiler  is 

a  metallic  vessel  in  which  steam  is  generated  under  pressure,  by  the 
application  of  heat.  The  essential  parts  of  a  steam  boiler  are  the 
the  furnace,  the  boiler  proper,  and  the  setting.  In  addition,  in  order 
to  operate  it,  every  boiler  must  be  provided  with  certain  auxiliaries 
such  as  a  chimney,  a  feed  pump,  a  pressure  gage,  a  water  column,  and 
suitable  piping,  valves,  etc.  The  sectional  view  in  Fig.  125  shows  a 


FIG.  125. — Longitudinal  and  transverse  sections  of  a  horizontal  return  tubular  boiler 

and  setting. 

standard  type  of  boiler,  known  as  the  horizontal  return  tubular  boiler. 
In  this  figure,  a  is  the  boiler  front,  which  is  usually  made  of  cast  iron. 
In  this  front  are  three  sets  of  doors,  set  b  being  termed  the  fire 
doors,  and  set  c  the  ash-pit  doors,  while  the  upper  doors  are  known  as 
clean-out  doors.  The  clean-out  doors  allow  access  to  the  front  end  of 
the  boiler,  for  cleaning.  D  is  a  brick  partition  termed  the  bridge  wall. 
Between  the  fire  doors  and  the  bridge  wall  are  placed  the  grates  E,  upon 
which  the  fire  is  built.  Back  of  the  bridge  wall  is  a  space  termed  the 
combustion  chamber.  The  boiler  proper  consists  of  a  cylindrical  drum 
with  flat  ends,  which  is  made  by  rolling  together  plates  of  steel  from 
1/4  to  5/g  of  an  inch  in  thickness,  and  riveting  to  the  ends  of  the  hollow 
cylinder,  so  formed,  circular  plates  termed  tube  sheets.  Extending 

234 


ART.  240 


THE  HORIZONTAL  WATER  TUBE  BOILER 


235 


from  the  front  to  the  rear  tube  sheets  are  rows  of  tubes,  about  three 
or  four  inches  in  diameter,  which  carry  the  gases  of  combustion  through 
the  water  space.  After  passing  along  the  under  side  of  the  boiler  and 
through  the  combustion  chamber,  the  hot  gases  from  the  fire  enter  the 
tubes  and  pass  forward  to  the  breeching  or  gas  passages  which  serve 
to  carry  them  to  the  chimney.  The  tubes,  as  will  be  seen  from  the 
transverse  section  of  the  boiler  and  setting,  occupy  the  lower  two- 
thirds  of  the  boiler,  while  the  upper  one-third  is  reserved  as  steam 
space.  The  boiler  is  filled  with  water  to  a  depth  of  about  three  inches 
above  the  tops  of  the  tubes.  When  the  boiler  is  in  operation,  this  water 


FIG.  126. — Longitudinal  section  of  a  horizontal  water  tube  boiler. 

has  the  temperature  of  vaporization  corresponding  to  the  pressure  of 
the  steam,  usually  from  300°  to  400°  F.  The  temperature  of  the  metal 
of  the  boiler  is  only  a  little  higher,  so  that  when  the  hot  gases  are  led 
along  the  under  side  of  the  shell,  and  back  through  the  tubes,  they  are 
promptly  cooled,  surrendering  their  heat  to  the  water,  and  evaporat- 
ing it. 

240.  The  Horizontal  Water  Tube  Boiler.  Fig.  126  shows  another 
type  of  boiler  which  is  known  as  a  horizontal  water  tube  boiler.  This 
differs  from  the  former  type  in  that  the  water  is  contained  in  a  number 
of  tubes  about  which  the  fire  and  hot  gases  are  caused  to  play.  These 


236 


THE  STEAM  BOILER 


ART.  241 


tubes  pass  from  the  rear  headers  to  the  front  headers,  and  their  contents 
are  caused  to  circulate  by  passing  forward  through  tubes  t-t,  upward 
through  the  front  headers  /,  rearward  through  the  drum  d,  and  down- 
ward through  the  tear  headers  r.  Since  the  rear  headers  contain  water 
only,  while  the  front  headers  contain  a  considerable  amount  of  steam 


n 


oooooo  oo 
oooooo  oooooo 
oooooo  oooooo 
oooooo  oooooo 


FIG.  127. — Transverse  and  longitudinal  sections  of  a  locomotive  type  boiler. 

in   the  form  of  foam  and  bubbles,  the  resulting  difference  in  density 
causes  this  circulation  to  go  on  with  a  considerable  velocity. 

241.  Classification  of  Boilers.  Various  other  types  of  boilers  are 
in  use,  but  they  all  consist  of  a  furnace,  either  of  firebrick,  or  of  metal 
surrounded  by  water,  of  heating  surfaces,  usually  in  the  form  of  tubes 


oooooooooo 
ooooo ooooo 
ooooooooooo 
ooooooooooo 


oooooooooo 
oooooooooo 

ooooooooooo 

ooooooooooo 

o  ooo 

o  ooooooo 

O  OOOOOO 

o  ooooo 


0000000^)00000000000 


--^  oooooooo 
ooooooo 
\ oooooo 


FIG.   128. — Transverse  and  longitudinal  sections  of  a  single  furnace  Scotch  marine 

boiler. 

surrounded  by,  or  containing  water,  and  of  gas  passages  which  bring 
the  furnace  gases  into  intimate  contact  with  the  heating  surfaces. 
They  also  contain  a  drum,  or  steam  storage  reservoir,  whose  function 
it  is  to  separate  the  water  from  the  steam  by  gravity,  so  that  dry  steam 
may  be  drawn  from  the  boiler. 


ART.  241 


CLASSIFICATION  OF  BOILERS 


237 


The  boilers  ordinarily  in  use  may  be  divided  into  three  classes. 
Boilers  of  the  first  class  are  known  as  fire  tube  boilers.  In  such  boilers 
the  flames  from  the  furnace  are  caused  to  pass  through  tubes  which  are 


238 


THE  STEAM   BOILER 


ART.  241 


as  water  tube  boilers.  In  such  boilers  the  heating  surface  consists  of 
tubes  surrounded  by  hot  gases  and  containing  water.  The  horizontal 
water  tube  boiler  already  described  is  of  this  type.  Sometimes  the 
tubes  are  in  a  vertical  position,  as  in  the  boiler  illustrated  in  Fig.  130, 
which  is  termed  a  vertical  water  tube  boiler,  and  sometimes  curved 
tubes  are  used,  as  in  the  boiler  illustrated  in  Fig.  131.  The  third  type 


FIG.  131. — Section  of  a  Stirling  water  tube  boiler. 

of  boiler  is  known  as  a  flash  boiler.  In  this  boiler  the  feed-water  which 
is  to  be  vaporized  flows  into  one  end  of  a  long  tube  which  is  heated, 
and  the  water  is  vaporized  before  it  has  passed  through  the  tube.  Such 
boilers,  being  light  for  their  power,  are  often  used  in  steam-driven  auto- 
mobiles. The  Parker  steam  generator,  illustrated  in  Fig.  132,  is  an 
illustration  of  such  a  boiler  adapted  for  stationary  service.  In  all  there 


ART.  242 


THEORY  OF  THE  STEAM   BOILER 


239 


are  several  hundred  types  of  boilers  in  use,  but  they  are  all  modifications 
or  combinations  of  the  three  types  mentioned. 

242.  Theory  of  the  Steam  Boiler.  When  the  gases  resulting  from 
combustion  leave  the  fire  they  have  a  high  temperature.  As  they  pass 
through  the  boiler,  encountering  metallic  surfaces  which  are  in  contact 
with  hot  water,  they  are  reduced  in  temperature.  Finally,  after  passing 
through  the  boiler,  they  are  discharged  into  the  chimney  at  a  temper- 
ature very  much  less  than  the  temperature  of  the  fire,  but  still  consider- 
ably higher  than  the  temperature  of  the  water  in  the  boiler.  The  rate 
at  which  they  will  impart  heat  to  any  surface  with  which  they  are  in 


FIG.  132. — Section  of  a  Parker  down-flow  boiler  with  superheater. 

contact  is  proportional  to    the  difference  in  temperature  between  the 
gases  and  the  surfaces,1  so   that  they  lose  heat  the  most  rapidly  to  the 

1  The  assumption  sometimes  made,  that  the  rate  of  heat  transfer  is  proportional 
to  the  square  of  the  temperature  difference,  is  untenable.  The  resistance  encountered 
by  the  heat  in  its  passage  from  the  gas  to  the  water  may  be  divided  into  three  parts. 
The  first  and  largest  part  is  the  thermal  resistance  of  the  layer  of  cool  gases  which 
is  in  immediate  contact  with  the  heating  surface,  and  which  is  prevented  by  friction 
from  having  the  motion  of  the  main  body  of  gas.  The  second  part  is  the  resistance 
of  the  metal  plates,  which  is  very  small.  The  third  part  is  the  res' stance  of  a  thin 
layer  of  steam  which  separates  the  metal  plates  from  the  water.  Each  of  the  resist- 
ances must  follow  the  usual  law  of  heat  conduction,  which  is  that  the  rate  of  heat 
conduction  is  proportional  to  the  conductivity  (or  inversely  proportional  to  the 
specific  resistance)  of  the  material,  proportional  to  the  temperature  difference,  and 


240  THE  STEAM   BOILER  ART.  242 

first  surface  with  which  they  come  in  contact.  In  order  to  determine 
the  rate  of  heat  conduction,  and  the  final  temperature  of  the  gases 
leaving  a  boiler,  we  will  assume  that  a  quantity  of  hot  gas  is  flowing 
through  a  tube  surrounded  by  water;  that  the  initial  temperature  of 
the  gas  as  it  comes  from  the  fire  is  Tft  that  the  diameter  of  the  tube  is 
3.82  inches,  so  that  the  surface  exposed  to  the  action  of  the  gas  per 
foot  of  length  of  the  tube  is  one  square  foot ;  that  the  gas,  when  in  con- 
tact with  the  tube,  will  impart  to  it  H  heat  units  per  square  foot  per 
hour  for  each  degree  difference  in  temperature  between  the  gas  and 
the  tube;  that  the  temperature  of  the  inner  surface  of  the  tube  Tw  is 
sensibly  the  same  as  the  temperature  of  the  water ;  and  that  W  pounds 
of  gas  pass  each  cross-section  of  the  tube  per  hour.  If  the  gases  flow 
through  a  certain  section  of  the  tube  whose  length  is  dL,  and  the  difference 
in  temperature  between  the  gases  passing  this  section  and  the  tube 
itself  is  T,  they  will  be  reduced  in  temperature  while  passing  the  section 
by  the  amount  dT.  The  quantity  of  heat  imparted  to  the  water  through 
the  walls  of  this  section  of  the  tube  will  be  HTdL  heat  units  per  hour. 
The  heat  lost  by  the  gas  passing  this  section  in  one  hour  will  be  equal 
to  the  change  in  temperature  dT,  times  the  specific  heat  at  constant 
pressure,  times  the  weight  of  gas  passing  the  cross-section  each  hour. 
Writing  these  quantities  equal  we  will  have 

dTCpW (1) 


Assuming  the  length  of  the  tube  to  any  point  to  be  L  feet,  we  will  have, 
since  dT  is  negative, 

r™  * /v (*) 

J  T  L  Lp  W  Jo 

Integrating  this  we  have 

Tf-Tw'     HL 

loge—  =  r    w-     • ^3) 

l  u2j  W 

Clearing  we  have 

L'p  \\ 

Solving  for  T 

'  =  \oge(Tf-Tw)  -  7,  -^ (5) 


inversely  proportional  to  the  thickness  of  the  material.  This  law  has  been  thoroughly 
established  by  experiment,  and  any  other  assumptions  will  be  found  to  lead  to  results 
which  are  mutually  inconsistent.  Experiments  which  have  tended  to  establish  the 
idea  that  the  rate  of  heat  transmission  is  proportional  to  the  square  of  the  temper- 
ature difference  have  invariably  been  so  conducted  as  not  to  eliminate  the  effects 
or  radiation. 


ART.  243         THE  EFFICIENCY  OF  THE  HEATING  SURFACE  241 

We  may  write  this,  for  simplicity, 

\0gT  =  A-B±,  (6) 


in  which 


and        B=A3~,  (7) 


and  the  logarithms  are  common,  and  not  natural  logarithms. 

243.  The  Efficiency  of  the  Heating  Surface.  The  principal  item  in 
the  cost  of  boiler  operation  is  the  cost  of  the  fuel  burned.  It  is  therefore 
highly  desirable  to  use  the  least  possible  quantity  of  fuel  in  generating 
a  given  quantity  of  steam.  To  do  this,  we  must  of  course  transfer  to 
the  water  in  the  boiler  the  greatest  possible  proportion  of  the  heat 
generated  by  the  combustion  of  the  fuel  in  the  furnace.  If  we  disregard 
(as  is  permissible  in  most  practical  cases)  the  latent  heat  of  the  water 
vapor  formed  by  combustion,  we  find  that  the  heat  generated  in  the 
furnace  is  equal  to  the  theoretical  rise  in  temperature  of  the  products 
of  combustion,  multiplied  by  the  water  equivalent  of  the  flue  gas.  The 
theoretical  rise  in  temperature  is  of  course  equal  to  the  difference 
between  the  theoretical  fire  temperature  Tf,  and  the  temperature  of 
the  fire  room,  Ta.  The  amount  of  heat  lost  to  the  chimney  is  equal 
to  the  difference  between  the  temperature  of  the  flue  gas  Tc  and  the 
temperature  of  the  fire  room  Ta,  multiplied  by  the  water  equivalent  of 
the  flue  gas.  The  heat  utilized  by  the  boiler  will  then  be  equal  to  the 
difference  between  the  theoretical  fire  temperature  and  the  temperature 
of  the  flue  gas,  multiplied  by  the  water  equivalent  of  the  flue  gas.  Since 
the  temperature  of  the  flue  gas  is  equal  to  the  temperature  of  the  water 
in  the  boiler  plus  the  final  difference  in  temperature  between  the  water 
and  the  gas,  we  may  write 

Tc=  TW+T  ........  '.     .     (1) 

In  order  to  find  the  theoretical  efficiency  of  the  heating  surface  of  a 
boiler,  we  must  divide  the  heat  transferred  to  the  water  by  the  heat 
generated  by  the  combustion,  in  which  case  we  will  obtain  the  equation 

rii          rii  rii          rii  rii 

lf-lc  _    lj-J_w-^ 

'  .......      Z 


An  inspection  of  the  above  equation  will  show  that  the  efficiency 
of  the  heating  surface  may  be  increased  by  increasing  the  theoretical 
fire  temperature,  since  such  an  increase  adds  the  same  quantity  to  both 
numerator  and  denominator  of  the  fraction.  The  efficiency  of  the 
heating  surface  may  also  be  increased  by  reducing  the  temperature 
difference  between  the  water  and  the  gases  leaving  the  boiler,  and  by 
increasing  the  temperature  of  the  air  supplied  to  the  fire. 


242  THE  STEAM  BOILER  ART.  244 

244.  Nominal  Power  of  a  Boiler.     The  rate  of  driving  of  a  boiler 
may  be  defined  as  the  quantity  of  heat  transferred  from  the  hot  gas 
to  the  water  per  square  foot    of    heating  surface  per  hour.     When  the 
percentage  of  radiation  loss  is  small,  this  is  very  nearly,  although  not 
exactly,  proportional  to  the  rate  of  evaporation,  or  the  number  of   pounds 
of  water  actually  evaporated  per  square  foot  of  heating  surface  per  hour. 
In  discussing  the  theoretical  efficiency  of  boilers,   in  this  chapter  the 
rate  of  driving  will  be  assumed  to  be  proportional  to  the  rate  of  evapo- 
ration.    Usual  practice  allows  about   10  to   12  square  feet  of  heating 
surface  per  nominal    boiler    horse-power.      A  boiler  horse-power  is  the 

&  capacity  to  evaporate  34.5  pounds  of  water  per  hour  from  and  at 
212°,  which  requires  the  transmission  of  33,480  B.T.U.  per  hour  from 
the  gas  to  the  water.  It  will  be  seen  that  at  the  usual  rating,  the  heating 
surface  of  a  boiler  is  required  to  transmit,  on  the  average,  about  3000 
B.T.U.  per  square  foot  per  hour.  This  may  be  considered  the  normal 
rate  of  driving,  and  other  rates  of  driving  will  be  expressed  as  a  per 
cent  of  the  normal  rate. 

An  increase  in  the  quantity  of  coal  burned  on  the  grate  of  a  boiler 
furnace  will,  of  course,  increase  the  quantity  of  heat  supplied  to  the 
boiler  in  a  given  time.  The  rate  of  heat  supply  is  proportional  to  trie 
rate  of  combustion,  which  may  be  defined  as  the  number  of  pounds  of 
coal  burned  per  square  foot  of  grate  per  hour.  The  number  of  pounds 
of  gas  per  hour  passing  through  the  boiler  (the  quantity  W  in  equation 
(5),  Art.  242)  is  proportional  to  the  rate  of  combustion,  and  may  be 
found  by  multiplying  the  rate  of  combustion  by  one  plus  the  number 
of  pounds  of  air  per  pound  of  fuel,  and  the  product  by  the  grate  area.  The 
rate  of  driving  of  a  given  boiler  is  proportional  to  the  product  of  the 
rate  of  combustion  into  the  efficiency  of  the  boiler  at  that  rate  of  driving. 

245.  Temperature  of  the  Flue  Gas.     Referring  again  to  equation  (5)  . 
Art.  242,  we  may,  since  the  heating  surface  in  square  feet  is  equal  to 
the  length  of  the  tube  in  feet,  write  it  in  the  form 


in  which  T  is  the  temperature  difference  between  the  water  in  the  boiler 
and  the  gases  leaving  the  boiler,  Tf  is  the  temperature  of  the  water  in 
the  boiler,  H  is  the  number  of  heat  units  transmitted  per  hour,  per 
square  foot  of  heating  surface  per  degree  difference  in  temperature, 
from  the  gas  to  the  water,  F  is  the  number  of  square  feet  of  heating 
surface  in  the  boiler,  W  the  number  of  pounds  of  gas  passing  through 
the  boiler  per  hour,  and  the  logarithms  are  common  and  not  natural 
logarithms.  Plotting  the  relation  between  the  amount  of  heating  sur- 


ART.  246        CONDITIONS  OF  MAXIMUM  BOILER  EFFICIENCY 


24.1 


face  and  the  final  temperature  of  the  gases  for  a  constant  rate  of  com- 
bustion, we  will  have  the  curve  illustrated  in  Fig.  133. 

An  inspection  of  this  curve  shows  that  the  temperature  of  the  gas 
flowing  through  the  tube  continually  approaches,  but  never  reaches, 
the  temperature  of  the  water,  Tw  (i.e.,  T  approaches  zero).  We  will 
also  find  that  while  the  reduction  in  temperature  is  rapid  at  first,  it 
finally  becomes  slow  and  that  further  increase  of  the  heating  surface 
does  not  produce  any  material  reduction  in  the  temperature  of  the  gas 
leaving  the  boiler.  We  may  therefore  conclude  the  following  in  regard 
to  the  efficiency  of  the  heating  surface  of  a  boiler:  First,  the  portion 
of  the  chimney  loss  which  is  due  to  the  difference  in  temperature  between 
Tf  and  TWj  may  be  reduced  to  any  desired  extent  by  sufficiently  increasing 
the  heating  surface  of  the 
boiler.  Second,  there  is  a  200° 

1900 

practical  limit  to  the  desirable  »•  1800 
extension  of  the  heating  sur- 
face, since  if  this  surface  is 
made  too  great,  the  amount 
of  heat  transferred  through 
that  portion  of  the  surface 
last  encountered  by  the  gas 
will  be  too  'small  to  be  of 
practical  use.  Third,  the 
higher  the  initial  temperature 
of  the  gases  (i.e.,  the  greater 
the  temperature  of  the  fire), 
the  greater  the  proportion  of 
the  total  heat  generated  in 
the  furnace  which  may  be 
transferred  to  the  water. 
Fourth,  the  less  the  weight 

of  gases  passing  through  the  boiler  each  second  (i.e.,  the  less  the  rate 
of  combustion),  the  greater  the  proportion  of  their  total  heat  which  will 
be  transferred  to  the  water.  Fifth,  the  greater  the  conductivity  of  the 
heating  surface  (i.e.,  the  greater  the  value  of  H)}  the  greater  the  efficiency 
of  the  boiler. 

246.  Conditions  of  Maximum  Boiler  Efficiency.  It  will  thus  be  seen 
that  in  order  to  operate  a  boiler  at  maximum  efficiency,  it  is  necessary  that 
the  quantity  of  air  supplied  per  pound  of  fuel  shall  be  a  minimum,  since 
a  low  ratio  of  air  to  fuel  will  give  a  high  furnace  temperature,  and  also 
will  reduce  the  weight  of  gases  passing  through  the  boiler  in  a  given 
time.  An  appreciable  increase  in  the  conductivity  of  the  heating  sur- 
faces can  only  be  obtained  by  reducing  the  thickness  of  the  film  of  cold 


012345 
Sq.  Ft.  of  Heating  Surface  per  Lb.  Coal  Burned 

FIG.  133. — Relation  between  the  rate  of  combus- 
tion and  the  temperature  of  the  flue  gas. 


244 


THE  STEAM  BOILER 


ART.  247 


gases  in  contact  with  the  heating  surface.  This  may  be  done  by  arranging 
the  gas  passages  of  the  boiler  in  such  a  way  that  the  streams  of  gas 
shall  be  thoroughly  broken  up  and  intermingled  at  every  possible  point, 
thus  bringing  fresh  supplies  of  hot  gas  into  contact  with  the  heating 
surface.  It  has  been  suggested  that  this  will  be  best  accomplished  by 
drawing  the  gases  through  the  boiler  at  high  velocity  and  reducing  the 
area  of  the  gas  passages.  It  has  also  been  suggested  that  an  excess  of 
air  be  deliberately  added  to  the  gases  in  order  to  increase  their  velocity, 
or  that  a  portion  of  the  flue  gases  be  re-circulated  for  the  same  reason. 
When  these  methods  are  tested  in  practice,  however,  they  prove  to 
be  defective.  In  case  the  passages  are  greatly  restricted  and  a  power- 
driven  fan  is  employed  to  draw  the  air  through  at  high  velocity, 
it  is  found  that  the  value  of  the  power  taken  by  the  fan  exceeds  the 
value  of  the  increased  efficiency  of  the  boiler,  so  that  the  system  is  com- 
mercially less  efficient  than  the  common  method  of  boiler  operation. 
If  the  quantity  of  gases  is  increased,  the  loss  of  efficiency  due  to  the  extra 
weight  of  these  gases  circulated  is  greater  than  the  gain  realized  by  the 
more  thorough  contact  secured  (i.e.,  W  in  the  equation  in  Art.  245  increases 
as  fast  as,  or  faster  than  H ,  as  might  be  expected) .  None  of  these  schemes 

are  practically  as  satisfactory  as 
a  further  addition  of  heating 
surface  would  be  in  securing 
an  increase  in  efficiency,  and  the 
addition  of  an  economizer  as 
described  in  Chapter  XVI,  or 
an  air  preheater,  is  even  more 
satisfactory. 

247.  Effect  of  Rate  of  Driving 
on   the  Efficiency  of  the  Heating 
Surface.     Substituting  the  value 
of     T     as     obtained     from     Fig. 
133,   in    equation    (2),    Art.    243, 
and    solving    for     the    efficiency, 
sq.  Ft.  of  Heading  surface  per  Lb7.  of  coal9     we    obtain    the   curve    given    in 
FIG.    134.-Relation  between   the  efficiency    FiS-  .  134>     which     Sives     ^    the 
and  the  rate  of  combustion.  relation    between    the    efficiency 

of    the    heating    surface    and  the 

amount  of  heating  surface  for  a  constant  rate  of  combustion.  This 
same  curve  also,  of  course,  shows  the  relation  between  the  efficiency 
of  the  heating  surface  and  the  rate  of  combustion  when  the  amount 
of  heating  surface  remains  constant.  It  will  be  seen  that,  as  the 
heating  surface  is  increased,  or  the  rate  of  combustion  reduced,  the 
efficiency  of  the  heating  surface  increases  slowly,  approaching,  but 


100 

f 

§80 

> 


r>0 


10 


ART.  248 


EFFECT  OF  AIR  LEAKAGE 


245 


never  equaling  the  value 


E  = 


The  curve  in  Fig.  135  shows  the  "relation  between  the  rate  of  driving 
and  the  efficiency  of  the  heating  surface.  Inspection  shows  that  the 
efficiency  falls  off  more  rapidly  for  a  given  percentage  increase  in  the 
rate  of  driving,  than  for  the  same  percentage  increase  in  the  rate  of 
combustion. 


100 


90 


80 


a  so 

"o 
>> 
§40 

0) 


10 


2000  4000  6000  8000 

B.T.U.per  Hr.  per  Sq.  Ft.  of  Heating  Surface. 

FIG.  135. — Relation  between  efficiency  and  rate  of  driving. 


10,000 


248.  Effect  of  Air  Leakage.     The  effect  of  an  increase  in  the  num- 
ber of  pounds  of  air  per  pound  of  fuel  upon  the  efficiency  of  a  boiler  is 
shown  in  the  two  curves  in  Fig.  136.     The  dotted  curve  shows  the  rela- 
tion when  the  rate  of  combustion  is  constant,  while  the  full  line  shows 
the  relation  when  the  rate  of  driving  is  constant.     It  will  be  noted  that 
an  increase  in  the  ratio  of  air  to  fuel  has  a  more  serious  effect  in  reducing 
the  efficiency  of  the  boiler  than  any  of  the  other  elements  affecting  this 
efficiency,  for  the  range  of  values  commonly  found  in  practice. 

249.  Effect  of  Increasing  the  Conductivity  of  the  Shell.     An  increase 
in  the  conductivity  of  the  boiler  plates  is  equivalent  to  an  extension 
of  the  boiler  surface.     This  explains  why  the  removal  of  scale  from  a 


246 


THE  STEAM  BOILER 


ART.  250 


boiler  does  not  very  greatly  increase  the  efficiency  of  a  boiler,  although 
it  may  considerably  increase  the  conductivity  of  the  heating  surface. 
At  the  normal  rates  of  driving  even  a  considerable  reduction  in  the 
resistance  of  the  heating  surface  to  the  passage  of  heat,  has  very  little 
effect  upon  the  efficiency  of  the  boiler,  just  as  at  the  normal  rate  of 
driving  a  considerable  increase  in  the  heating  surface  will  have  but 


100 


10  15  20  25  30 

Lbs.  of  Air  per  Lb.  of  Coal . 


35 


40 


FIG.  136. — Relation  between  the  efficiency  and  the  ratio  of  air  to  fuel. 

Curve    I  is  for  a  constant  rate  of  combustion. 
.Curve  II  is  for  a  constant  rate  of  driving. 

little  effect  upon  the  efficiency.  An  increase  in  the  pressure  of  the 
steam,  and  therefore  of  the  temperature  of  the  water  in  the  boiler,  has 
but  little  effect  upon  the  efficiency  of  the  boiler,  as  may  be  seen  by 
reference  to  Fig.  137,  which  shows  the  relation  between  the  temperature 
of  the  steam  and  the  efficiency  of  the  boiler,  for  the  conditions  given. 

250.  Effect  of  Radiation  on  Boiler  Efficiency.  A  boiler,  like  any 
other  heated  body,  radiates  a  considerable  amount  of  heat  into  the 
surrounding  air.  This  amount  may  vary  from  2  to  20  per  cent  of  the 
quantity  of  heat  generated  in  the  furnace  and  depends  upon  the  tem- 
perature of  the  boiler  and  furnace.,  and  the  thoroughness  with  which  the 


ART.  250        EFFECT  OF  RADIATION  ON  BOILER  EFFICIENCY 


247 


84 


83 


boiler  is  clothed  in  non-conducting  materials  and  the  area  of  radiating 
surface  exposed.     This  loss  by  ra- 
diation  is  independent,  or    almost 
so,  of  the  rate  of  driving. 

In  considering  the  efficiency  of 
the  boiler,  it  is  necessary  to  con- 
sider the  loss  due  to  radiation. 
The  surface  of  the  setting  in- 
creases with  the  square  of  the 
dimensions  of  the  boiler,  while 
the  heating  surface  of  the  boiler 
increases  with  the  cube  of  its  dimen- 
sions, hence  the  radiating  surface 
increases  in  proportion  to  the  two- 
thirds  power  of  the  heating  surface.  ^  1  Q_ 
m,  ,  •  ,.  .  FIG.  137.— Relation  between  the  efficiency 

The   loss   of   heat  due  to  radiation          and  the  temperature  of  evaporation, 
may  be  taken  as  being  independent 

of   the   rate   of   driving   and   proportional   to   the   radiating   surface,  or 
1001 — 


80 


79 


78 


\ 

\ 

\ 

x 

\ 

k 

\ 

c 

rs 

Sag 

» 

\ 

\ 

\ 

\ 

p 

=  200    Gag< 

\ 

200 


240         280          320         360 
Temperature  of  the  Steam. 


400 


90 

80 

70 

&60 


2000 


4000  6000  8000  10,000 

B.T.U.per  Sq-  Ft.  of  Heating  Surface  per  Hour. 


12,000 


FIG.  138. — Relation  between  the  efficiency  and  the  rate  of  driving,  allowing  for  radiation. 
Curve      I  is  for    5  per  cent  radiation  loss. 
Curve    II  is  for  10  per  cent  radiation  loss. 
Curev  III  is  for  15  per  cent  radiation  loss. 


248  THE  STEAM  BOILER  ART.  251 

to  the  two-thirds  power  of  the  heating  surface.  If  we  assume  that 
this  radiation  loss  in  a  boiler  of  normal  design  is  10  per  cent  of  the  heat 
generated  when  the  boiler  is  operated  at  the  normal  rate  of  driving, 
we  will  have  the  relation  between  the  efficiency  and  rate  of  driving 
shown  in  Fig.  138.  Curves  are  added  showing  the  relation  of  the  efficiency 
and  the  rate  of  driving  when  the  radiation  loss  is  5  per  cent  and  also 
15  per  cent  of  the  heat  generated  at  normal  load.  It  will  be  seen  from 
these  curves  that  there  is  a  definite  limit,  depending  upon  the  per  cent 
of  radiation  loss,  which  determines  the  most  efficient  rate  of  driving 
and  the  proper  allowance  of  heating  surface  per  boiler  horse-power.  It 
will  be  seen  that  a  boiler  with  an  excess  of  heating  surface  may  be  prac- 
tically less  efficient  than  a  smaller  boiler  which  is  operated  at  a  higher 
rate  of  driving,  besides  being  more  costly.  The  rate  of  driving  commonly 
adopted  at  the  present  time  is  that  rate  which  experience  shows  to 
give  the  best  efficiency. 

251.  Heat  Losses  in  a  Boiler   Plant.     The  heat  losses  incurred   in 
the  operation  of  a  boiler  plant  arise  from  four  sources.     The  first  source 
of  loss  is  caused  by  incomplete  combustion.     Such  loss  is  due  to  the 
dropping  of  unburned  coal  through  the  grates,  the  escape  of  unburned 
gases  to  the  stack,  etc.     The  second  source  of  loss  is  the  inefficiency 
of  the  heating  surface.     Loss  from  this  source  is  usually  termed  stack 
loss.     The  third  source  of  loss  is  radiation.     The  fourth  source  of  loss 
is  the  latent  heat  of  the  water  formed  by  combustion.     Loss  from  this 
source  is  usually  exceedingly  small. 

Improvement  in  the  efficiency  of  the  boiler  plant  must  be  looked 
for  from  the  following  sources:  By  improvement  in  the  management 
of  fires  and  the  construction  of  furnaces  we  may  increase  the  furnace 
temperature,  reduce  the  quantity  of  air  required  per  pound  of  fuel,  and 
reduce  the  loss  due  to  incomplete  combustion.  By  careful  arrangement 
and  construction  and  properly  clothing  the  boiler  in  non-conducting 
materials,  we  may  reduce  the  radiation  loss.  Whenever  the  radiation 
loss  is  sufficiently  reduced  to  warrant  it,  we  may  reduce  the  rate  of 
driving  by  increasing  the  heating  surface  per  boiler  horse-power.  Finally, 
we  may  so  arrange  the  gas  passages  and  heating  surfaces  that  the  gases 
are  brought  into  thorough  contact  with  the  heating  surfaces,  thus 
increasing  their  conductivity. 

252.  Distribution  of  Losses  as  Shown  by  a  Boiler  Test.    The  following  example 
will  serve  to  show  the  distribution  of  losses  in  a  boiler  and  the  method  of  computing 
these  losses  from  the  results  of   a  boiler  test.     The  coal  used  in  this  test  was  shown 
by  proximate  analysis  to  contain  4.5  per  cent  of  moisture,  16.0  per  cent  of  volatile 
matter,  71.1  per  cent  of  fixed  carbon,  and  8.3  per  cent  of  ash.     The  heating  value  as 
obtained  by  the  Parr  calorimeter  was  13,640  B.T.U.  per  pound.     The  analysis  of 
the  flue  gas  gave  for  CO2  10.0  per  cent,  for  O2  9.8  per  cent,  for  CO,  0.2  per  cent; 


ART.  252    DISTRIBUTION  OF  LOSSES  AS  SHOWN  BY  A  BOILER  TEST     249 

and  for  nitrogen,  by  difference,  80.0  per  cent.  The  total  weight  of  water  fed  to 
the  boiler  was  2832  pounds.  The  total  weight  of  coal  fired  was  469  pounds. 
59.0  pounds  of  ash  were  taken  from  the  ash  pit  at  the  end  of  the  test.  The  average 
temperature  of  the  feed-  water  was  73.5°  F.  The  average  steam  pressure  was  82.2 
pounds  absolute,  and  the  average  quality  of  the  steam  as  shown  by  the  throttling 
calorimeter  was  98.7  per  cent.  The  total  heat  available  from  the  combustion  of 
469  pounds  of  coal  was  6,390,000  B.T.U.  From  the  analysis  of  this  coal  8.3  per  cent 
or  39  pounds  is  incombustible.  Since  59  pounds  of  ash  fell  through  the  grates  during 
the  test,  20  pounds  of  this  must  have  been  unburned  carbon.  The  potential  heat 
contained  in  this  20  pounds  of  unburned  carbon  is  290,000  B.T.U.  The  heat  trans- 
ferred to  each  pound  of  water  evaporated  from  73.5°  and  at  82.2  pounds  absolute 
will  be,  since  the  quality  is  98.7  per  cent,  898.8  X  .987  +284-41.55  =  1120  B.T.U. 
The  heat  transferred  to  the  entire  quantity  of  water  evaporated  is  2832X1120  = 
3,170,000  B.T.U. 

The  remainder  of  the  heat  then  passed  up  the  chimney  in  potential  form  in 
unburned  gases,  or  was  carried  away  in  the  sensible  and  latent  heat  of  the  flue  gas, 
or  was  radiated  into  the  boiler  room  and  so  lost. 

From  the  flue  gas  analysis,  we  find  that  the  number  of  c.c.  of  oxygen  accounted 
for  in  100  c.c.  of  flue  gas  will  be 

9.8  +  10  +    ?  =  19.9  c.c. 


The  oxygen  represented  by  the  nitrogen  is 

.261X80  =  20.87  c.c. 

The  difference,  or  1.0  c.c.,  united  with  hydrogen  to  form  water.     The  number 
of  pounds  of  carbon  burned  per  pound  of  oxygen  supplied  was  equal  to 


The  number  of  pounds  of  hydrogen  burned  per  pound  of  oxygen  supplied  was 


80 
The  excess  of  air  was 

383X9.* 


-s-81.6%. 


80-3.83X9.8 
The  number  of  pounds  of  air  supplied  per  pound  of  combustible  was 


The  number  of  pounds  of  nitrogen  in  the  flue  gas  per  pound  of  combustible  was 


250  THE  STEAM  BOILER  ART.  252 

The  number  of  pounds  of  carbon  dioxide  in  the  flue  gas  per  pound  of  combustible 
was 

5.27X10.0  _ 
80 X. 2074  ~ 

The  number  of  pounds  of  carbon  monoxide  was 

3.36X0.2 


80  X. 2074 
The  number  of  pounds  of  water  vapor  was 

4.20X1.0 
80  X. 2074 

The  number  of  pounds  of  free  oxygen  was 

3.83X9.8 


80  X. 2074 


=0.04. 


-.25. 


=  2.27. 


Adding  the  water  equivalents  of  these  various  gases  we  will  have  5.274.     The 
latent  heat  of  evaporation  of  the  water  vapor  will  be  262  B.T.U. 
Each  pound  of  combustible  shown  by  the  flue  gas  consists  of 

.2014 

-^  -.-.  =.971  Ibs.  of  carbon. 

.2074 


and 

.0060 


=  .029  Ibs.  of  hydrogen. 


.2074 
The  heating  value  per  pound  of  combustible  will  then  be 

.971 X 14500  +  .029 X  62000  =  15880  B.T.U. 

Of  the  coal  burned  in  the  furnace  20  pounds,  or  4.26  per  cent,  dropped  through  the 
grates  in  the  form  of  unburned  carbon.  The  amount  of  heat  lost  in  this  manner  was 
.0426X14500-620  B.T.U.  per  pound  of  coal,  leaving  13640-620  =  13020  B.T.U. 
per  pound  of  coal  due  to  the  burning  of  combustible  substances  appearing  in  the  flue  gas. 
Dividing  this  quantity  by  15,880  we  will  have  .820  pounds  of  combustible  accounted 
for  in  the  flue  gas  for  1  pound  of  coal  fired.  The  total  weight  of  combustible  accounted 
for  in  the  flue  gas  will  therefore  be  .820X469  =  384.5  pounds. 

Since  the  boiler  room  temperature  is  70°,  and  the  stack  temperature  765°,  the 
flue  gases  will  be  rejected  at  a  temperature  695°  higher  than  their  original  tempera- 
ture. The  sensible  heat  carried  away  in  the  flue  gases  may  be  found  by  multiplying 
this  difference  in  temperature  by  the  water  equivalent  of  the  flue  gas  per  pound  of 
combustible  and  the  product  by  the  number  of  pounds  of  combustible  shown  by  the 
test  to  be  present  in  the  flue  gases.  This  gives 

695X5.274X384.5  =  1,410,000  B.T.U. 

The  latent  heat  carried  away  by  the  water  vapor  in  the  flue  gas  will  be 

262X384.5  =  101,000  B.T.U. 

The  number  of  B.T.U.  lost  as  potential  heat  in  the  CO  in  the  flue  gas  will  be 
.04X384.5X4380  =  67,400  B.T.U.  Adding  together  the  heat  lost  in  the  flue  gas, 
the  heat  imparted  to  the  water  and  the  heat  lost  by  incomplete  combustion,  we  will 


PROBS.  1-7 


PROBLEMS 


251 


have  5,038,000  B.T.U.  Subtracting  this  from  6,390,000  B.T.U.  which  was  the  total 
heat  supplied,  we  will  have  the  radiation  loss,  which  was  1,352,000  B.T.U.  Expressing 
these  various  heat  losses  as  percentages  of  the  total  heat  in  the  coal  fired,  we  will 
have  4.54  per  cent,  for  the  loss  through  the  grates,  49.6  per  cent  of  the  total  heat 
imparted  to  the  water,  22.05  per  cent  for  the  loss  in  the  sensible  heat  of  the  flue  gas, 
1.58  per  cent  for  the  loss  in  the  latent  heat  of  the  water  vapor  in  the  flue  gas,  1.05 
per  cent  for  the  loss  in  the  unburned  CO  and  21.2  per  cent  for  the  radiation  loss. 
The  radiation  loss  in  this  case  was  unusually  high,  since  the  boiler  was  a  vertical  fire 
tube  boiler  and  was  not  protected  by  any  non-conducting  covering,  the  plates  of 
the  boiler  being  exposed  to  the  air  of  the  fire  room.  The  distribution  of  heat  may  be 
tabulated  as  follows. 


B.T.U. 

Per  Cent. 

Heat  supplied  
Heat  utilized 

6,390,000 
3  170  000 

100 

49  6 

Stack  loss'  Sensible  heat                

1,410  000 

22.05 

Stack  loss;  Latent  heat  

101,000 

1.58 

Incomplete  combustion'   coal  through  grates 

290  000 

4  54 

Incomplete  combustion  ;  loss  in  CO  

67  400 

1.05 

Radiation  and  error 

1  352  000 

21  18 

The  efficiency  of  a  grate  is  found  by  subtracting  from  100  per  cent  the  heat  loss 
in  per  cent  due  to  the  unburned  carbon  which  drops  through  the  grate.  In  this  case 
the  efficiency  of  the  grate  was  100—4.54  =  95.46  per  cent.  The  efficiency  of  the  boiler 
and  grate  is  found  by  dividing  the  heat  imparted  to  the  water  evaporated  by  the 
total  heat  in  the  coal  fired.  The  efficiency  of  the  boiler  and  grate  in  this  case  was 
49.6  per  cent.  The  efficiency  of  the  boiler  is  found  by  dividing  the  efficiency  of  the 
boiler  and  grate  by  the  efficiency  of  the  grate.  In  this  case  the  efficiency  of  the  boiler 
was  51.9  per  cent. 

PROBLEMS 

1.  A   boiler  evaporates  steam   at  a  temperature   of  400°  F.     20  Ibs.  of  air  are 
used  per  pound  of  coal  (i.e.,  1  Ib.  of  coal  produces  21  Ibs.  of  flue  gas).     The  tempera- 
ture of  the  furnace  is  2400°  I4'.     Assuming  that  the  value  of  B  in  Eq.  (6)  in  Art.  242 
is  5.5  and  that  coal  is  burned  at  the  rate  of  1  Ib.  for  every  4   sq.ft.  of  heating  sur- 
face, find  the  probable  final  temperature  of  the  flue  gas.  Ans.     578°  F. 

2.  What  is  the  theoretical  efficiency  of  the  heating  surface  in  the  above  problem? 

Ans.     78% 

3.  A  boiler  contains  an  aggregate  of  1400  sq.ft.  of  heating  surface.      What  is  its 
nominal  horse  power?  Ans.     117. 

4.  How  many  Ibs.  of  water  will  it  evaporate  per  hour  into  steam  of  98  per  cent 
quality  at  a  pressure  of  100  Ibs.  gage  from  feed-water  at  a  temperature  of  70°,  at  rated 
load.  Ans.     3,46C  Ibs. 

5.  How  many  square  feet  of  grate  surface  will  be   required  for  the  above  boiler, 
if  20  Ibs.  of  coal  of  13,000  B.T.U.  are  burned  per  square  foot  of  grate,  and  the  boiler 
is  assumed  to  be  of  70  per  cent  efficiency.  Ans.     21.5  sq.  ft. 

6.  What  will  be  the  final  temperature  of  the  flue  gases  in  Problem  1,  if  the  rate 
of  combustion  be  doubled?  Ans     997°  F. 

7.  What  will  be  the  theoretical  efficiency  of  the  heating  surfaces  in  this  case? 

ADS.     64.5%. 


CHAPTER  XVI 
BOILER  PLANT  AUXILIARIES 

253.  The  Chimney.  Height  Required.  The  chimney  is  a  device 
for  producing  a  draft  or  difference  of  air  pressure,  which  is  utilized  to 
force  air  through  the  fire,  and  thence  through  the  furnace,  the  boiler 
itself,  and  the  breeching  through  which  the  furnace  gases  are  discharged 
into  the  chimney.  The  chimney  depends  for  its  operation  upon  the 
difference  in  weight  of  the  column  of  gas  which  it  contains,  and  of  a 
column  of  equal  height  and  cross-section  of  the  outside  air.  The  weight 
of  a  column  of  flue  gas  or  air  of  unit  cross-section  is  proportional  to 
the  barometric  pressure,  to  the  absolute  temperature  of  the  gas  or  air, 
and  to  the  height  of  the  column.  Let  H  be  the  height  in  feet  of  the 
top  of  the  chimney  measured  from  the  grates,  Ta  be  the  absolute  tem- 
perature of  the  atmosphere,  Tc  be  the  mean  absolute  temperature  of 
the  chimney  gases,  B  be  the  normal  barometric  reading  in  inches  of 
mercury  for  the  region  in  which  the  chimney  is  erected,  N.  be  the  per 
cent  of  CO2  in  the  flue  gas,  and  D  be  the  draft  produced  or  required, 
measured  in  inches  of  water.  The  weight  of  one  cubic  foot  of  air  will 
be,  from  the  characteristic  equation  of  gases 


the  pressure  in  pounds  per  square  foot  will  be 

P  =  70.7215  .........     (2) 

The  density  of  carbon  dioxide  is  1.  52  X  that  of  air.  Consequently,  the 
density  of  the  flue  gas  will  be  increased  by  .0052  for  every  per  cent  of 
carbon  dioxide  present.  Therefore  the  weight  of  one  cubic  foot  of 
flue  gas  will  be 

lb,,    .     (3) 


and  the  weight  of  a  column  one  foot  square  and  H  feet  high  will  be 

(l 

•*  C 


252 


ART.  254  DRAFT  REQUIRED  BY  A  BOILER  PLANT  AT  NOMINAL  LOAD  253 

The  weight  of  a  column  of  external  air,  one  square  foot  in  cross-section, 
and  H  feet  high,  will  be 

1.329  B  H  .. 
— yi Ibs (5) 

The  difference  in  pressure  produced  at  the  base  of  the  chimney  in  pounds 
per  square  foot  is  therefore 


Since  a  column  of  water  one  inch  high  produces  a  pressure  of  5.19  pounds 
per  square  foot,  the  draft  produced  by  the  chimney  will  be 


(7) 


Solving  the  above  equation  for  H,  in  order  to  find  the  height  of  chim- 
ney required  to  produced  a  given  draft  we  will  have 


In  the  absence  of  more  definite  data  we  may  assume  that  in  most 
actual  cases  of  chimneys  serving  boiler  plants  without  economizers, 
under  normal  atmospheric  conditions  we  will  have  for  the  draft  produced. 

D=.Q07H, (9) 

and  for  the  required  height  of  chimney, 

H=14QD (XO) 

254.  Draft  Required  by  a  Boiler  Plant  at  Nominal  Load.  When 
air  or  gas  flows  through  a  restricted  passage,  a  difference  of  pressure 
is  required  to  give  it  motion,  both  to  give  the  air  velocity,  and  in  order 
to  overcome  friction.  It  follows,  therefore,  that  in  its  passage  through 
the  fire,  the  boiler,  the  damper,  the  breeching  and  the  chimney,  the 
flue  gas  encounters  at  every  point  a  resistance  to  its  motion.  The  resist- 
ance is  measured  by  the  difference  in  pressure  required  to  move  the 
gas  through  the  passage  considered,  and  is  shown  by  experiment  to 
be  nearly  proportional  to  the  1.8  power  of  the  quantity  of  the  gas 
passing  in  a  given  time.  When  a  boiler  and  furnace  of  ordinary  design 
are  operated  at  their  rated  capacity,  we  find  that  the  difference  in  pressure 
required  to  draw  air  through  the  fire  is  from  .10  to  .30  inches  of  water. 
The  former  figure  is  for  free-burning  bituminous  coal  consumed  at  the 
rate  of  24  pounds  of  coal  per  square  foot  of  grate,  and  the  latter  figure  is 
for  anthracite  buckwheat  consumed  at  half  this  rate.  These  are  the 


254  BOILER  PLANT  AUXILIARIES  ART.  255 

usual  rates  of  combustion  in  furnaces  properly  designed  for  burning 
these  fuels  when  operated  at  their  rated  capacity.  The  resistance  of 
the  furnace  and  boiler  passages  to  the  current  of  gases,  ranges  from  .15 
to  .30  inches  of  water,  approaching  the  lower  value  in  the  case  of 
small  boilers  and  of  water  tube  boilers,  and  the  higher  one  in  the  case 
of  large  boilers  and  of  fire  tube  boilers.  Unless  the  breeching  is  excep- 
tionally long  and  tortuous,  its  resistance  will  range  from  .05  to  .20 
inches  of  water.  The  resistance  offered  by  the  chimney  itself,  when 
properly  designed  and  operating  at  rated  load,  ranges  from  10  per  cent 
to  20  per  cent  of  the  total  draft  produced,  and  includes  the  difference 
in  pressure  required  to  produce  the  actual  velocity  of  the  gases  in  the 
chimney.  The  total  draft  required  of  a  chimney  operating  a  boiler 
plant  at  rated  load  ranges  from  .40  to  1.00  inches  of  water,  according 
to  the  character  of  the  plant  and  the  kind  of  fuel,  and  in  most  practical 
cases  the  draft  required  will  be  between  .55  and  .75  inches  of  water. 
255.  Draft  Required  by  a  Boiler  Plant  when  Operating  at  an  Over- 
load. If,  however,  it  is  desirable  or  necessary  to  operate  the  plant, 
or  any  part  of  it,  at  more  than  rated  load,  the  chimney  must  be  of 
sufficient  height  to  provide  a  greater  draft  than  is  called  for  in  normal 
service.  After  the  draft  required  to  operate  the  plant  at  rated  load 
has  been  ascertained,  we  may  compute  the  maximum  draft  required 
by  the  formula 

/Maximum  Load  \  1>8 
r  rotated  Load     / 

in  which  D  is  the  draft  required  for  the  maximum  overload,  and  Dr 
is  the  draft  required  at  rated  load.  From  the  above  it  will  be  seen 
that  at  25  per  cent  overload  the  draft  required  will  be  1.50/)r,  at  50 
per  cent  overload  it  will  be  2.0SDr,  and  at  100  per  cent  overload  it  will 
be  3.50Z)r.  In  practice  it  has  been  found  that  the  minimum  height 
of  chimney  which  will  give  satisfaction  with  plants  of  normal  design, 
ranges  from  80  feet  in  the  case  of  free-burning  bituminous  coal  to  200 
feet  in  the  case  of  anthracite  slack;  heights  which  give  under  ordinary 
atmospheric  conditions  a  draft  of  from  .55  to  1.4  inches  of  water  and 
permit  overloads  of  about  10  per  cent.  It  is  usual  in  the  case  of  plants 
burning  anthracite  coal  of  small  size  to  assist  the  chimney  by  a  steam 
jet  or  fan  blower.  The  jet  or  blower  furnishes  the  excess  of  pressure 
necessary  to  force  the  air  through  the  fire,  while  the  chimney  serves  only 
to  draw  the  gases  through  the  boiler  passages  and  breeching  and  prevent 
their  escape  into  the  fireroom.  Were  it  not  for  this,  the  height  of 
chimney  required  to  produce  a  reasonable  overload  capacity  in  such 
plants  would  be  excessive.  Chimneys  above  200  feet  in  height  are  not 
therefore  usually  required  in  practice,  nor  are  they  economical  to  build. 


ART.  256  REQUIRED  DIAMETER  OF  CHIMNEYS  255 

They  are  sometimes  necessary,  however,  in  order  to  discharge  smoke 
or  noxious  gases  at  such  a  height  that  their  discharge  will  be  harmless. 

It  may  be  remarked  that  when  a  boiler  plant  operates  at  an  over- 
load, the  temperature  of  the  chimney  gases  is  increased,  which  makes 
the  overload  capacity  of  a  chimney  rather  more  than  theory  would 
indicate.  If  the  top  of  a  chimney  is  properly  formed,  wind  increases 
the  draft,  and  if  there  is  no  wind,  the  column  of  hot  air  rising  above 
the  chimney  acts  to  increase  its  effective  height.  Chimneys,  especially 
hort  chimneys  of  large  cross-section,  may  therefore  be  expected  to 
give  a  somewhat  greater  draft  than  theory  would  indicate. 

256.  Required  Diameter  of  Chimneys.  From  experiment  it  is  known 
that  the  loss  of  pressure  which  a  fluid  suffers  in  passing  from  one  point 
to  another  in  a  tube  of  uniform  diameter  is  directly  proportional  to 
the  distance  between  the  points  and  to  the  1.8  power  of  the  velocity 
of  the  fluid,  and  inversely  proportional  to  the  1.3  power  of  the  diameter 
of  the  tube.  This  loss  also  depends  upon  the  density  and  viscosity  of 
the  fluid  and  the  character  of  the  inner  surface  of  the  tube,  but  the 
proportionality  factor  for  any  given  tube  and  for  any  given  fluid  of  a 
constant  density  is  a  constant  quantity.  Applying  this  law  to  the  case 
of  a  chimney  we  will  find  that  the  draft  required  to  produce  a  given 
velocity  of  the  chimney  gases,  will  be 

1-8 

....  .     .    -     (1) 


in  which  Dc  is  the  draft,  in  inches  of  water,  required  to  produce  the 
given  velocity;  H  is  the  height  of  the  chimney  in  feet,  V  is  the  velocity 
of  the  chimney  gases  in  feet  per  second,  and  d  is  the  diameter  of  chimney 
in  inches.  Solving  equation  (1)  for  V  we  will  have 


v 


If  we  make  the  allowable  loss  of  draft  in  the  chimney  some  fraction 
of  the  total  draft  which  the  chimney  will  produce,  then  since  the  total 

draft  is  proportional  to  the  height  of  the  .chimney,  we  may  replace  ~ 
by  a  constant,  and  obtain  the  equation 


K2d-72  .......     (3) 

Since  the  capacity  of  the  chimney  is  proportional  to  the  product 
of  the  velocity  of  the  flue  gases  and  the  area  of  the  cross-section  (which 
is  proportional  to  d2)  we  may  write 

2).  (4) 


256  BOILER  PLANT  AUXILIARIES  ART.  257 

In  which  HP  is  the  nominal  capacity  of  the  chimney,  in  terms  of  the 
boiler  horse-power  which  it  will  serve.  Solving  equation  (4)  for  the 
diameter  of  the  chimney,  we  will  have 

d  =  K  (HP)'37 (5) 

A  study  of  chimneys  of  good  proportion  giving  satisfactory  service 
shows  that  the  value  of  the  constant  K  should  be  about  5.5,  in  which 
case  the  resistance  of  the  chimney  to  the  passage  of  the  gases,  at  rated 
load,  is  about  15  per  cent  of  the  total  draft  produced,  in  the  case  of 
plants  of  rather  poor  economy.  Therefore  in  order  to  find  the  total 
draft  required  in  the  case  of  a  chimney  designed  by  this  formula,  we 
must  multiply  the  draft  found  by  equation  (1)  in  Art.  255  by  1.17. 
In  order  to  facilitate  computation  equation  (5)  may  be  written  in  the  form 

log  d=. 37  log  HP  +  .75.    . (6) 

in  which  d  is  the  diameter  of  the  chimney  in  inches,  and  HP  is  the 
nominal  horse-power  of  the  boiler  plant  which  it  is  to  serve. 

257.  Effect  of  Overloading  the  Boiler  Plant  upon  the  Capacity  of  the 
Chimney.  In  case  a  chimney  designed  by  the  above  rule  is  called  upon  to 
handle  a  greater  quantity  of  flue  gas  than  that  for  which  it  was  designed,  more 
than  15  per  cent  of  the  total  draft  must  be  utilized  in  overcoming  the  resistance 
of  the  chimney  itself.  Since  the  resistance  of  the  chimney  is  proportional  to  the  1.8 
power  of  the  velocity  of  the  gases,  the  amount  of  draft  required  to  overcome  the 
resistance  of  the  chimney  will  be 

D.        -i  c  M  /actual  load\  l>8 
J-'c  —  -15  Lf  [  -    ,   _.  ! — -j- I      , 
\  rated  load  / 

in  which  Dc  is  the  draft  required  to  overcome  the  resistance  of  the  chimney  and  D 
is  the  total  draft  produced  by  the  chimney. 

It  has  already  been  noted  that  chimneys  are  usually  made  of  sufficient  height  to 
provide  a  s.mall  overload  capacity,  usually  from  10  to  25  per  cent.  If  it  is  desired 
to  increase  the  power  of  a  boiler  plant  and  yet  to  use  the  old  chimney  in  carrying 
away  the  gases,  this  excess  of  height  affords  an  opportunity  for  increasing  the  capacity 
of  the  plant  by  reducing  slightly  the  overload  capacity  of  the  individual  units.  If 
D  equals  the  total  draft  available,  in  inches  of  water,  and  Df  be  the  amount  of  draft 
required  to  overcome  the  resistance  of  the  fire,  the  boiler  and  the  breeching  when 
the  individual  boilers  are  operated  at  the  desired  rating,  the  difference  is  available 
for  overcoming  the  resistance  of  the  chimney.  If  this  difference  is  greater  than  15 
per  cent  of  the  total  draft  produced,  the  capacity  of  the  chimney  will  exceed  that 
given  by  Equation  (4),  Art.  2c6.,  and  the  ratio  of  the  capacities  will  equal  the  1.8 
root  of  the  ratio  of  the  draft  actually  available  for  overcoming  the  chimney  resistance 
to  that  assumed  in  equation  (6)  to  be  available.  Writing  this  as  an  equation  we  will  have 


in  which  HPa  is  the  nominal  rating  of  the  boilers  which  the  chimney  will  serve  under 
the  assumed  conditions  of  overload,  HPr  is  the  rating  of  the  chimney  from  formula 


ART.  258  EXAMPLE  OF  CHIMNEY   DESIGN  257 

4  Art.  256,  D  is.  the  total  draft  the  chimney  will  produce,  and  Df  is  the  resistance  of 
the  furnace,  boiler  and  breeching,  when  operated  under  the  assumed  conditions  of 
overload. 

258.  Example  of  Chimney  Design.  The  following  example  will  serve  to  make 
clear  the  application  of  the  principles  developed  above.  A  chimney  is  required  to 
burn  buckwheat  anthracite  in  a  region  where  the  normal  barometer  reading  is  28 
inches,  and  the  normal  summer  temperature  70°.  The  plant  will  be  required  to 
develop  about  25  per  cent  overload  and  is  of  1000  horse-power  nominal  capacity. 
Assume  the  temperature  of  the  gases  to  be  500°  F.,  and  the  per  cent  of  CO2  to  be 
10  per  cent. 

The  draft  required  by  the  fire  at  normal  load  =  .30". 

The  draft  required  to  overcome  the  boiler  resistance  at  normal  load  =  .25". 

The  draft  required  to  overcome  the  resistance  of  the  breeching  at  normal  load 
=  .10. 

The  sum  of  the  above  =  . 65". 

Draft  required  to  overcome  resistance  of  chimney  =  . 65" X. 175  =  .12". 

Total  draft  required  at  rated  load  =  .77". 

Total  draft  required  at  25  per  cent  overload  =  .77"X  1.251'8  =  1.15". 
Substituting  the  proper  values  in  formula  8,  Art.  253,  for  the  height  of  chimney,  we 
will  have 

#  =  3.905—  -^L,  .v  - 194  ft. 


0  960 

In  order  to  find  the  diameter  of  this  chimney,  we  use  equation  (5),  Art.  256,  which 
gives 

d  =  5.5X1000'37=72  inches. 

Should  it  be  desirable  to  extend  this  plant  at  any  future  time,  its  power  may  be 
greatly  increased,  provided  the  individual  units  are  not  required  to  carry  25  per 
cent  overload.  If  they  are  required  to  carry  rated  load  merely,  the  nominal  power 
of  the  station  will  be,  according  to  the  formula  in  Art.  257, 


. 

.l/o  X  .60 


=  2280  horse-  power. 


259.  The  Injector.  An  injector  is  an  apparatus  for  forcing  water 
against  pressure  by  utilizing  the  impact  of  a  jet  of  steam.  The  apparatus 
is  shown  in  principle  in  Fig.  139,  in  which  A  is  a  pipe  supplying  steam 
to  the  nozzle  B,  in  which  the  steam,  expanding  adiabatically,  acquires 
a  high  velocity.  The  jet  of  steam  from  this  nozzle  passes  through  the 
tube  C,  which  is  known  as  a  combining  tube,  anpl  in  doing  so  carries 
with  it  any  air  in  the  neighborhood.  As  a  result  a  vacuum  is  created 
which  sucks  the  water  through  the  suction  pipe.  D  into  the  chamber 
surrounding  the  jet.  As  soon  as  the  steam  comes  in  contact  with  the 
water  so  drawn  in,  it  is  instantly  condensed  and  imparts  its  momentum 
to  the  water,  forcing  it  into  the  combining  tube.  The  water  issuing 
from  the  combining  tube  in  the  form  of  a  jet  passes  into  a  third  tube 
E,  which  is  known  as  the  discharge  tube,  in  which  its  velocity  is  trans- 


258  BOILER  PLANT  AUXILIARIES  ART.  260 

formed  into  pressure.  After  passing  through  the  discharge  tube,  the 
water  flows  through  a  check  valve  and  into  the  boiler  or  other  region 
into  which  it  is  desired  to  force  it.  Before  the  current  of  water  is 
established  the  water  escapes  around  the  space  between  the  combining 
and  the  discharge  tubes  and  flows  away  through  an  opening  F,  termed 
the  overflow.  As  soon,  however,  as  a  solid  stream  of  water  of  suffi- 
ciently high  velocity  is  flowing  through  the  combining  tube,  no  water 
will  escape  through  the  overflow. 


FIG.  139. — Diagram  of  an  injector. 

260.  Efficiency  of  the  Injector.  In  order  to  illustrate  the  principle  of  the  injector, 
we  will  assume  one  taking  dry  and  saturated  steam  at  a  pressure  of  100  pounds 
absolute  and  delivering  the  water  against  the  same  pressure.  Assume  that  the 
absolute  pressure  within  the  suction  chamber  is  10  pounds  per  square  inch.  The 
kinetic  energy  of  the  jet,  per  pound  of  steam  flowing,  is  127,000  foot-pounds,  its 
velocity  is  2840  feet  per  second,  and  its  momentum  2840  pounds  feet  per  second. 
The  head  against  which  the  water  is  discharged  is  (100  — 10)  X 2.31  =208  feet.  Allow- 
ing 25  per  cent  excess  for  friction  we  will  have,  say,  250  feet.  The  velocity  of  the 
jet  issuing  from  the  combining  tube  must  be 


F  =  v'20/i=v'64.4X250  =  128  ft.  per  sec. 

The  momentum  of  the  jet,  which  is  composed  of  x  pounds  of  water  and  1  pound 
of  steam,  must  from  the  principles  of  mechanics,  be  equal  to  that  of  the  steam  jet. 

Hence  (1+^)128  =  2840, 

and  a:  =  21. 2  pounds  of  water  pumped  per  pound  of  steam  supplied. 
The  work  done  per  pound  of  steam  is 

21.2X250  =  5300  ft.-lbs. 

The  efficiency  of  the  injector  as  a  pump,  is  therefore  only 

5300 
127400  =4-15  per  cent, 

of  the  efficiency  of  a  Rankine  cycle  engine  working  through  the  same  pressure 
range.  It  will  be  seen  from  the  above  example  that  as  a  pump  the  injector  is  very 
inefficient,  although  all  of  the  heat  of  the  steam  is  returned  to  the  boiler.  Of  the 
kinetic  energy  of  the  steam  jet,  only  from  3  to  6  per  cent  is  available  to  force  the 
water  into  the  boiler,  the  remainder  being  transformed  into  heat  as  a  result  of  the 
inelastic  impact  of  the  steam  upon  the  water. 


ART.  261 


BOILER  FEED-PUMPS 


259 


The  injector  is  often  a  troublesome  instrument  to  operate,  since  the  condition  of 
the  apparatus  must  be  perfect  before  it  will  give  satisfactory  service.  The  stoppage 
of  any  of  its  small  passages  by  a  piece  of  coal  or  by  the  accumulation  of  scale 


FIG.  140. — Boiler  feed  pump. 

renders  it  inoperative.  It  is  commonly  used  in  the  case  of  locomotive  and  port- 
able boilers,  but  is  not  usually  used  in  stationary  service.  Many  modifications  of  the 
injector  are  in  use  and  are  known  by  different  names.  In  some  modifications,  one 
injector  is  arranged  so  as  to  deliver  water  to  the  suction  chamber  of  a  second  injector, 
such  an  injector  being  known  as  an  inspirator  or  a  double  tube  injector. 

261.  Boiler  Feed-pumps.  Boilers  are  usually  supplied  with  feed- 
water  by  means  of  a  direct-acting  steam  pump,  such  as  is  illustrated 
in  Fig.  140.  These  pumps  are  of  various  types,  but  almost  all  of  them 
use  steam  non -expansively  and  are  very  wasteful.  The  exhaust  from  these 
pumps,  however,  is  usually  employed  to  heat  the  feed-water,  and  on 


FIG.  141. 

this  account  no  loss  is  experienced  from  their  use,  since  they  return  to 
the  boiler  all  of  the  heat  which  is  taken  for  their  operation.  Of 
late  years,  in  places  where  economizers  are  installed,  motor-driven  centrif- 
ugal pumps  have  been  used  for  boiler  feeding.  Such  a  pump  is  illustrated 
in  Fig.  141.  These  pumps  are,  of  course,  practically  as  economical  as 


260 


BOILER  PLANT  AUXILIARIES 


ART.  2G2 


are  the  main  engines  themselves.  They  run  at  nearly  constant  speed, 
maintaining  a  constant  pressure  in  the  delivery  pipe  and  the  quantity 
of  water  delivered  and  power  required  automatically  adjust  themselves 
to  the  needs  of  the  boiler  for  feed-water. 

262.  Feed-water  Heaters.  In  order  to  avoid  losses  incident  upon 
supplying  a  boiler  with  cold  feed-water,  the  heat  of  the  exhaust 
steam  of  the  engines  and  pumps  is  usually  utilized  for  heating  the 
feed-water.  A  gain  of  from  10  to  12  per  cent  may  be  realized  under 
usual  conditions  by  using  a  feed -water  •  heater. 
Feed-water  heaters  are  of  two  kinds,  known  as 
closed  and  open  heaters.  In  the  closed  heaters, 
the  water  to  be  heated  is  usually  forced  through 
tubes  which  are  surrounded  by  the  exhaust 
steam,  which  does  the  heating.  Such  a  heater 
is  shown  in  section  in  Fig.  142.  Sometimes  the 
water  surrounds  the  tubes  and  the  exhaust 
steam  passes  through  them.  In  open  heaters, 
the  feed-water  is  brought  into  direct  contact 
with  the  exhaust  steam.  Usually  the  water- 
coming  from  an  open  heater  is  a  few  degrees 
hotter  than  that  coming  from  a  closed  heater. 
The  theory  of  heat  transfer  in  the  closed  heater 
is  the  same  as  in  the  case  of  the  surface  con- 
denser, and  they  may  be  designed  by  the  same 
principles. 

The  following  problem  will  serve  to  illustrate 
the  economy  obtained  by  the  use  of  a  heater. 
Assume  that  a  boiler  operates  at  a  pressure 
165  pounds  absolute,  that  the  feed -water  sup- 
plied has  a  temperature  of  70°  and  that  by 
the  use  of  a  suitable  heater  the  feed  temperature  may  be  raised 
to  205°.  The  total  heat  which  must  be  imparted  to  the  feed -water 
in  evaporating  it  from  70°  at  165  pounds  is  found  by  subtracting 
the  heat  of  the  liquid  at  70°  from  the  total  heat  of  the  steam  at  165 
pounds.  In  the  same  way,  the  heat  required  when  the  heater  is 
used  will  be  found  by  subtracting  the  heat  of  the  liquid  at  205°  from 
the  total  heat  of  the  steam.  We  find  in  one  case  1156.9  B.T.U.  are 
required,  while  in  the  other  case  only  1022.0  B.T.U.  are  required,  showing 
that  if  the  heater  is  adopted,  the  quantity  of  fuel  required  by  the  boiler 
in  a  given  time  will  be  reduced  more  than  11.7  per  cent,  since  not  only 
is  less  heat  needed  to  evaporate  the  required  quantity  of  water,  but 
the  rate  of  driving  of  the  boiler  is  decreased,  and  therefore  the  efficiency 
of  the  boiler  plant  is  improved. 


FIG.  142. — Section  of  a 
closed  heater. 


ART.  263  THE  ECONOMIZER  261 

263.  The  Economizer.  The  economizer  is  an  apparatus  which 
utilizes  the  waste  heat  of  the  flue  gases  to  heat  the  water  entering  the 
boiler.  It  is  possible  by  the  use  of  a  suitable  economizer  to  reduce  the 
temperature  of  the  chimney  gases  to  within  200°  of  the  temperature 
of  the  feed-water  and  to  heat  the  water  entering  the  boiler  practically 
to  the  temperature  of  vaporization.  It  will  be  seen  that  the  use  of  the 
economizer  will  very  greatly  reduce  the  fuel  required  for  a  given  quantity 
of  steam  generated.  Economizers  are  usually  built  with  cast-iron  tubes 
and  headers,  and  are  provided  with  sliding  rings  which  scrape  the  soot 
from  the  tubes.  When  an  economizer  is  used,  it  is  usually  necessary 
to  use  a  fan  to  create  the  necessary  draft,  since  the  temperature  of  the 
gases  entering  the  chimney  is  not  sufficiently  high  to  cause  a  good  draft. 

The  theory  of  the  heat  transfer  in  the  economizer  is  different  from 
that  of  the  boiler,  .since  the  water  entering  the  economizer  is  at  a  low 
temperature  and  it  gradually  increases  as  it  passes  through  the  economizer. 
The  current  of  hot  gases  flows  through  the  economizer  in  the  opposite 
direction  to  the  current  of  the  water,  so  that  the  hottest  gases  come  into 
contact  with  the  water  entering  the  boiler  and  the  coolest  gases  into 
contact  with  the  water  entering  the  economizer.  By  this  means  the 
temperature  of  the  gases  leaving  the  economizer  may  be  reduced  below 
the  temperature  of  the  water  entering  the  boiler. 

The  difference  in  temperature  between  the  flue  gases  and  the  water 
varies  at  different  points  in  the  economizer,  usually  being  greater  at 
the  end  next  the  boiler  than  at  the  cool  end  of  the  economizer.  The 
water  equivalent  of  the  flue  gas  discharged  per  second  by  the  boiler 
is  usually  less  than  the  weight  of  the  feed-water  supplied  to  the  boiler 
in  the  same  time.  It  will  be  seen  therefore  that  the  fall  in  temperature 
of  the  flue  gases  between  any  two  points  in  the  economizer  will  be  greater 
than  the  rise  in  temperature  of  the  feed-water  and  the  less  the  excess 
of  air  used  for  combustion  the  more  pronounced  will  be  this  effect. 

It  is  usual  to  supply  from  3^  to  5  square  feet  of  economizer  surface 
per  boiler  horse-power.  When  an  economizer  is  so  proportioned,  the 
feed-water  entering  the  boilers  is  usually  heated  to  about  300°  F.  The 
.Greene  Economizer  Company  give  the  following  empirical  formula  for 
the  rise  in  temperature  of  the  feed-water  in  passing  through  an  economizer : 


in  which  x  =  the  rise  in  temperature  of  the  feed-water; 

771  =  the  temperature  of  flue  gas  entering  the  economizer; 
ti  =  temperature  of  feed-water  entering  economizer; 


262  BOILER  PLANT  AUXILIARIES  ART.  264 

w  =  pounds  of  feed-water  per  boiler  horse-power  per  hour; 
G  =  pounds  of  flue  gas  per  pound  of  combustible; 
C  =  pounds  of  coal  burned  per  boiler  horse-power  per  hour; 
y  =  square  feet  of  economizer  heating  surface  per  boiler  horse- 
power. 

264.  The  Superheater.  The  use  of  superheated  steam  in  connection 
with  the  steam  turbine  is  becoming  very  common  on  account  of  the 
great  gain  in  efficiency  resulting  therefrom.  Superheaters  may  form  a 
part  of  the  boiler  and  be  heated  by  the  gases  on  their  way  through 
the  boiler.  Many  superheaters,  however,  are  independently  fired,  having 
their  own  furnace  and  gas  passages.  The  use  of  a  superheater  in  con- 
nection with  a  boiler  plant  does  not  directly  affect  the  efncienc}^  of  the 
boiler  plant.  It  does,  however,  permit  the  use  of  a  small  boiler  plant, 
since  less  steam  will  be  required  from  a  boiler  plant  equipped  with 
superheaters,  on  account  of  the  greater  efficiency  of  the  engines.  In  case 
the  size  of  the  boiler  plant  is  not  reduced,  the  effect  of  the  introduction 
of  superheaters  will  be  to  reduce  the  rate  of  driving  and  so  increase 
the  efficiency  of  the  boilers. 

Superheaters  are  usually  formed  of  heavy  seamless  steel  tubing, 
expanded  into  forged  steel  headers  and  sometimes  protected  by  cast- 
iron  rings  from  the  direct  action  of  the  hot  gases.  A  superheater 
requires  greater  care  in  its  operation  than  is  usually  required  with  a 
boiler,  since  the  superheaterelements  are  not  filled  with  water,  and 
therefore  are  easily  overheated.  The  conductivity  of  a  unit  area  of 
superheater  surface  is  considerably  less  than  that  of  the  same  area  of 
boiler-heating  surface,  since  the  heat  is  transferred  from  the  metal  to  a 
gas  or  superheated  vapor  in  the  case  of  a  superheater,  while  it  is 
transferred  from  the  metal  to  a  liquid  in  the  case  of  a  boiler. 

The  amount  of  superheater  surface  required  per  boiler  horse-power 
varies  according  to  the  required  temperature  of  the  steam,  and  the 
temperature  of  the  gases  in  contact  with  the  superheater  surface.  The 
following  empirical  formula  has  been  proposed  by  J.  E.  Bell : 

105 


2(T-t)-S' 

in  which    x  =  the  number  of  square  feet  of  superheater  surface  per  boiler 

horse-power; 

/S  =  the  superheat  in  degrees  F; 
T  =  the  temperature  of  the  flue  gases  at  the  point  where  the 

superheater  is  located ; 
i  =  the  temperature  of  the  saturated  steam. 


PROBS.  1-7  PROBLEMS  263 


PROBLEMS 

1.  What  height  of  chimney  will  be  required  to  give  a  draft  of  1.2  inches  of  water 
under  ordinary  operating  conditions  ?  Ans.     168  ft. 

2.  A  boiler  plant  having  a  stack  100  ft.  high  will  operate  satisfactorily  when 
evaporating  10,000  Ibs.  of  water  per  hour.     To  what  height  must  the  stack  be  raised 
in  order  that  the  plant  shall  evaporate  12,000  Ibs.  of  water  per  hour  ?     Ans.    139  ft. 

3.  What  diameter  of  chimney  will  be  required  for  a  boiler  plant  of  2000  horse- 
power ?  Ans.     91  inches. 

4.  A   non-condensing    engine  f  is   used   in   connection   with   a  feed-water  heater. 
Without  the  heater,  the  temperature  of  the  feed  is  65°.     With  the  heater,  the  tem- 
perature of  the  feed  is  190°.     What  per  cent  of  coal  is  saved  when  the  heater  is 
employed?     The  boiler  generates  steam  at  a  pressure  of  80  Ibs.  gage  and  of  98%  quality. 

Ans.     10.8%. 

5.  The  feed-water  heaters  of  a  plant  bring  the   temperature  of  the  feed  to  160°. 
When  an  economizer  is  employed  the  temperature  of  the  feed  is  brought  to  280°. 
What  per  cent  of  coal  is  saved  by  the  economizer  if  the  boilers  produce  dry  and 
saturated  steam  at  a  pressure  of  165  Ibs.  absolute?  Ans.     11.2%. 

6.  An  economizer  is  required  to  raise   the   temperature  of  the  feed-water  100°. 
The  temperature  of  the  feed  is  150°,  the  temperature  of  the  flue  gas  entering  the 
economizer  is  600°,  the  boilers  require  30  Ibs.  of  feed-water  per  horse-power  per  hour, 
4  Ibs.  of  coal  are  burned  per  horse-power  per  hour,  and  20  Ibs.  of  flue  gas  are  produced 
per  Ib.  of  coal.     Find  the  number  of  square  feet  of  economizer  surface  required  per 
boiler  horse-power.  Ans.     2.98  sq.ft. 

7.  A  superheater  is  required  to  superheat  steam  of  a  pressure  of  180  Ibs.  absolute, 
100°.   The  temperature  of  the  gases  is  1300°.    Find  the  number  of  square  feet  of  super- 
heater surface  required  per  boiler  horse-power.  Ans.     0.57  sq.ft. 


CHAPTER  XVII 
WATER-COOLING   APPARATUS 

265.  Advantage   of   Using   Water-cooling   Apparatus.      Condensing 
water  is  usually  taken  from  lakes  or  streams,  or,  at  the  seaboard,  from 
the  sea.     When  a  power  plant  is  erected  at  some  point  distant  from  a 
stream  or  other  body  of  water,  the  plant  may  be  made  non-condensing, 
or  it  may  be  provided  with  some  method  for  cooling  the  condensing  water. 
A  condensing  plant  not  provided    with  any  method  for  cooling  water 
usually  requires   from   300   to   500   pounds    of    condensing    water    per 
horse-power  per   hour,    and    a    non-condensing   plant   usually    requires 
from  25  to  35  pounds  of  water  per  horse-power  per  hour,  while  a  conden- 
sing plant  equipped  with  a  cooling  apparatus  will  require  only  from  12 
to  18  pounds  of  water  per  horse-power  per  hour.     Hence,    in   all   those 
cases  where  the  plant  is   large   and    cooling   water  is   expensive,    either 
because  only  small  quantities  of  water  are  available,  or  city  water  must 
be  purchased,  water-cooling  apparatus   is    a   necessary  adjunct  to  the 
plant.     The  use  of  the  cooling  tower  or  other  water-cooling  device  not  only 
permits  of  economy  in  the  consumption  of  water,  but  also  of  fuel,  since  a 
condensing  plant  will  use  only  from  one-half  to  two-thirds  of  the  quantity 
of  fuel  required  by  a  non-condensing  plant  of  the  same  power. 

266.  The  Cooling  Pond.     The  simplest  method  of  cooling  condensing 
water  is  to  construct  an  artificial  pond  having  an  impervious  bottom  from 
which  the  cooling  water  is  drawn,  and  into  which  it  is  discharged  aiter 
passing  through  the  condenser.     The  evaporation  from  the  surface  of 
the  pond  and  radiation  of  heat  from  the  water  into  the  surrounding   air 
will  keep  the  temperature  of  the  water  down  in  spite  of  the  fact  that 
heat  is  being  continually  added  to  it.  The  water  must  of  course  be  replaced 
as  fast  as  it  evaporates.     The  pond  must  be  of  sufficient  area  so  that  the 
evaporation  may  go  on  at  a  rate  which  will  dispose  of  the  heat  imparted 
to  it  without  allowing  the  temperature  of  the  cooling  tower  to  become 
too  great.     The  area  required  will  depend  upon  the  mean  summer  tem- 
perature, upon  the  dryness  of  the  air,  upon  the  character  and  amount 
of  the  load  of  the  station,  upon  the  depth  of  the  water,  and  upon  the  amount 
of  wind  which  may  ordinarily  be  expected  in  the  region.     The  rate  of 
evaporation  and  consequently  the  rate  at  which  the  water  is  cooled  is. 
of  course,  proportional  to  the  area  of  water  surface  exposed,  so  that, 

264 


ART.  267    RATE  OF  EVAPORATION  FROM  THE  SURFACE  OF  WATER      265 

other  things  being  equal,  the  area  of  the  pond  must  be  proportional  to 
the  power  of  the  station.  The  higher  the  summer  temperature  of  the 
region,  the  warmer  the  water  in  the  pond  must  be  for  a  given  rate  of 
evaporation  per  square  foot  of  surface.  During  cold  winter  weather, 
although  evaporation  proceeds  at  a  slower  rate  than  in  summer,  the  pond 
will  lose  heat  more  rapidly  on  account  of  radiation  into  the  surrounding 
cold  air.  The  humidity  of  the  atmosphere  and  the  amount  of  wind  to  be 
expected  is  also  a  very  important  factor  in  settling  the  size  of  the  pond. 
If  the  air  is  dry,  the  water  will  evaporate  rapidly  from  the  surface  of 
the  pond,  while  if  the  climate  is  humid,  the  evaporation  will  proceed 
slowly.  If  the  load  upon  the  station  is  constant,  the  depth  of  water  in 
the  pond  makes  no  particular  difference.  If,  however,  the  load  is  variable, 
a  much  smaller  pond  may  be  made  to  serve  if  the  water  is  deep,  since 
this  large  mass  of  water  will  serve  as  a  heat  reservoir;  absorbing  the 
heat  during  the  periods  of  peak  load,  with  a  small  rise  in  temperature, 
and  slowly  recovering  its  normal  temperature  during  the  periods  of  light 
load. 

267.  Rate  of  Evaporation  from  the  Surface  of  Water.  The  rate  of 
evaporation  per  square  foot  of  water  surface  exposed  to  air  is,  in  theory, 
proportional  to  the  difference  between  the  quotient  of  the  square  root 
of  the  absolute  temperature  of  the  water  into  the  density  of  saturated 
steam  at  that  temperature,  and  the  quotient  of  the  square  root  of  the 
absolute  temperature  of  the  air  into  the  density  of  the  water  vapor  present 
in  the  air.1  We  may,  therefore,  in  engineering  computations,  take  the 
rate  of  evaporation  per  square  foot  of  surface  as  being  proportional  to 
the  difference  between  the  saturation  pressure  of  water  vapor  at  the 
temperature  of  the  water  and  the  actual  pressure  of  the  water  vapor 
in  the  air.  It  has  been  found  that  in  still  air 2  the  difference  in  pressure 
required  to  evaporate  1  pound  of  water  per  square  foot  of  water  surface 
per  hour  is  about  3.2  pounds  per  square  inch.  In  cllse  a  brisk  wind  is 
blowing  over  the  surface,  the  rate  of  evaporation  will  be  from  four  to  six 
times  as  great  as  is  given  by  the  above  rule.  The  following  problem 
will  serve  to  illustrate. the  principle: 

Assume  that  the  temperature  of  the  water  is  80°,  that  the  temperature 
of  the  air  is  70°,  and  that  the  humidity  is  60  per  cent.  The  saturation 
pressure  at  80°  is  0.505  pounds  per  square  inch.  The  pressure  of  the 
water  vapor  in  the  atmosphere  is  0.36X0.60  =  0,22  pounds  per  square 
inch.  The  difference  in  pressure  is  0.285  pounds  per  square  inch.  Since 
the  difference  in  pressure  required  to  evaporate  1  pound  of  water  per 

1  See  Chapter  XXVI. 

2  By  still  air  is  meant  air  in  which  the  only  currents  are  those  produced  by  the 
difference  in  density  of  hot  moist  air  and  cool  dry  air.     It  does  not  mean  air  in  which 
all  currents  are  prevented  by  artificial  enclosure. 


266  WATER-COOLING  APPARATUS  ART.  268 

square  foot  per  hour  is  about  3.2  pounds  per  square  inch,  a  difference 
of  pressure  of  1  pound  will  evaporate  0.30  pounds  of  water  per  square 
foot  per  hour  in  still  air.  The  rate  of  evaporation  from  the  surface  will 
be  in  this  case  0.285X0.30  =  0.085  pounds  per  square  foot  per  hour  in 
the  case  of  still  air. 

268.  Determining  the  Area  of  a  Cooling  Pond.  It  will  be  seen  from 
the  above  that  the  area  of  a  cooling  pond  required  for  a  given  station 
may  be  determined  in  the  following  manner.  From  the  records  of  the 
Weather  Bureau,  the  mean  summer  temperature  and  humidity  for  the 
region  may  be  found:  From  these  data,  the  mean  pressure  of  the  water 
vapor  in  the  atmosphere  may  be  determined  from  a  steam  table.  Assum- 
ing the  temperature  to  which  the  condensing  water  is  to  be  cooled,  find 
in  the  steam  table  the  saturation  pressure  corresponding  to  this  temperature 
and  from  it  deduct  the  mean  summer  pressure  of  the  water  vapor  in  the 
air.  Multiplying  the  difference-  so  obtained  by  0.30  we  will  have  the 
quantity  of  water  evaporated  per  hour  per  square  foot  of  surface  from  the 
cooling  pond.  Dividing  this  quantity  into  the  average  quantity  of  steam 
rejected  per  hour  by  the  engines  of  the  station,  we  will  have  the  required 
area  of  the  cooling  pond  in  square  feet.  Good  condensing  plants  will 
on  the  average  require  an  evaporation  of  15  pounds  of  water  per  horse- 
power per  hour  from  the  cooling  pond. 

The  total  quantity  of  water  which  the  pond  must  evaporate  in  twenty- 
four  hours  may  be  found  by  multiplying  the  twenty-four-hour  factor 
of  the  station  by  its  rated  horse-power  and  their  product  by  15.  In 
case  it  is  known  that  the  station  is  likely  to  be  inefficient,  it  will  be  neces- 
sary to  allow  more  than  15  pounds  of  water  per  hour. 

The  following  problem  will  serve  to  illustrate  the  method  of  finding 
the  area  of  a  cooling  pond.  The  mean  summer  temperature  as  obtained 
from  the  Weather  Bureau  reports  is  75°,  and  the  humidity  60  per  cent. 
It  is  desired  to  coot  the  water  in  the  pond  to  80°.  The  station  is  to  be 
of  1000  rated  horse-power,  and  the  twenty-four-hour  load  factor  is  40 
per  cent.  From  the  steam  tables  the  pressure  of  saturated  water  vapor 
at  80°  is  0.505,  and  at  75°  temperature  and  60  per  cent  humidity  it  is 
0.429X0.60  =0.26  pounds  per  square  inch.  For  the  difference  we  will 
have  0.505  -O.26  =0.245.  The  rate  of  evaporation  will  then  be  0.245  X 
0.30=0.073  pounds  per  square  foot.  The  average  horse-power  of  the 
station  will  be  1000X0.40=400.  The  required  rate  of  evaporation  will 
be  400X15=6000  pounds  per  hour.  The  cooling  surface  will  then  be 

6000 

——=82,000  square  feet,  or  the  pond  required  will  be  approximately 

.073 

290  feet  square. 

The  cooling  surface  allowed  in  the  above  pond  is  82  square  feet  per 
rated  horse-power.  Since  82  square  feet  of  water  will  weigh  about  5100 


ART.  269  THE  SPRAY  POND  267 

pounds  for  every  foot  in  depth,  it  will  be  seen  that  a  comparatively  shallow 
pond  will  serve  to  carry  great  overloads  for  a  short  period  of  time.  Allow- 
ing 600  pounds  of  condensing  water  per  horse-power  per  hour,  it  will  be 
seen  that  the  above  pond  will  contain  8^  hours'  supply  of  condensing 
water  for  eveiy  foot  of  depth.  It  is  generally  well  to  make  the  pond 
deep  enough  to  carry  from  twelve  to  twenty-four  hours'  supply  of  con- 
densing water,  allowing  600  pounds  per  horse-power  per  hour  at  the  rated 
horse-power  of  the  station.  If  the  above  pond  be  made  2  feet  deep, 
the  quantity  of  water  contained  will  be  ample. 

It  may  be  seen  from  the  above  computations  that  a  cooling  pond 
must  be  quite  large.  For  small  powers,  say  up  to  500  horse-power,  the 
cooling  pond  is  a  cheap  and  simple  method  of  solving  the  problem  of 
condensing  water  supply,  provided  land  is  cheap.  In  case  land  is  expensive 
or  the  station  is  large,  the  spray  pond  or  cooling  tower  will  be  a  preferable 
method  for  obtaining  a  supply  of  condensing  water. 

269.  The  Spray  Pond.     A  second  method  of  cooling  condensing  water 
is  by  spraying  the  water  into  the  air  over  the  surface  of  the  small  pond, 
which  may  be,  and  quite  often  is,  placed  upon  a  roof  of  a  building.     In 
case  the  water  is  sprayed  into  the  air  in  this  way,  the  required  area  of 
the  pond  is  very  much  less  than  when  spraying  is  not  used,  but  since  the 
quantity  of  water  contained  in  the  pond  is  small,  it  is  necessary  to  provide 
sufficient  capacity  to  take  care  of  the  peak  load  of  the  station. 

270.  Area  of  Spray  Pond  Required.      When  water  is  sprayed  in  this 
manner,  it  will  be  cooled  by  evaporation  from  the  surface  of  the  drops, 
and  since  the  surface  exposed  by  the  drops  is  vastly  greater  than  the 
surface  of  the  same  quantity  of  water  exposed  in  a  pond,  the  evaporation 
will  be  very  much  more  rapid.     The  final  temperature  of  the  water  will, 
of  course,  be  higher  than  the  temperature  of  the  dew  point,  and  it  will 
be  found,  as  a  usual  thing,  that  the  pressure  of  saturated  water  vapor 
of  the  final  temperature  of  the  water  will  be  about  0.15  pounds  per  square 
inch  higher  than  the  pressure  of  the  water  vapor  in    the    atmosphere. 
Thus,  if  water  be  sprayed  into  air  having  a  temperature  of  70°,  and  a 
humidity  of  70  per  cent,  the  pressure  of  the  water  vapor  in  the  air  will  be 
0.70  X0.36  =0.25  pounds  per  square  inch.     The  temperature  of  the  water 
will  then  be  reduced  to  the  temperature  corresponding  to  the  pressure 
of  0.25+0.15  =  0.40  pounds  per  square  inch.     From  the  steam  tables, 
this  temperature  is  73°.     In  case  the  drop  in  temperature  of  the  water 
is  large,  (i.e.,  above  40  or  50°  F.),  it  will  be  found  that  air  in  the  neighbor- 
hood will  become  so  saturated  with  moisture  that  the  evaporation  will 
not  take  place  freely,  in  which  case  it  may  be  necessary  to  spray  the  water 
twice  in  order  to  bring  it  to  a  sufficiently  low  temperature.     It  will  usually 
be  found  preferable  to  use  such  a  quantity  of  water  that  the  required 
reduction  in  temperature  will  not  exceed  40°.     One  square  foot  of  pond 


268  WATER-COOLING  APPARATUS  ART.  271 

surface  will  be  sufficient  for  the  cooling  of  200  pounds  of  water  (about 
3  per  cent  of  which  will  be  evaporated)  and  the  spray  nozzles  should  be 
placed  a  sufficient  distance  apart  so  that  each  will  be  allowed  the 
area  given  by  the  above  rule.  It  will  usually  be  found  that  3 
square  feet  of  pond  surface  per  horse-power  will  suffice,  but  the  total 
surface  provided  on  such  a  basis  must  be  estimated  on  the  maximum  and 
not  the  rated  or  mean  horse-power  of  the  station.  If  the  efficiency  of 
the  station  is  low,  so  that  the  quantity  of  heat  rejected  per  horse-power 
is  more  than  is  required  to  evaporate  15  pounds  of  water,  the  surface 
allowed  per  horse-power  must  be  suitably  increased. 

271.  Power  Required  by  Spray  Nozzles.      When  condensing  water  is 
cooled  by  the  use  of  a  spray  pond,  it  is  necessary  to  pump  the  water  to 
the  spray  nozzles  at  a  pressure  of  from  15  to  20  pounds  per  square  inch. 
This  takes  a  considerable  amount  of  power.     Assuming  that  3  per  cent 
is  evaporated  and  that  the  quantity  is  15»  pounds  per  horse-power  per 
hour,  it  will  be  seen  that  the  quantity  pumped  per  horse-power  will  be 
about  500  pounds.     If  this  water  be  pumped  against  a  head  of  46  feet 
(which  corresponds  to  a  pressure  of  20  pounds  per  square  inch)  and  the 
efficiency  of  the  pumping  plant  be  60  per  cent,  the  work  required  to  do 
this  pumping  will  be  38,300  foot-pounds  per  hour,  or  0.019  horse-power. 
The  power  required  for  pumping  will  therefore  be  between  1J  and  2  per 
cent  of  the  power  of  the  station.     In  case  steam  pumps  are  used  for  this 
purpose,  and  they  are  run  condensing,  an  extra  allowance  of  water  must 
be  made  for  them,  since  such  pumps  are  much  less  efficient  than  large 
engines,  and  the  estimated  evaporation  of  15  pounds  of  water  per  horse- 
power per  hour  will  not  be  sufficient  to  furnish  them  with  cool  condensing 
water. 

272.  The  Cooling  Tower.     In  large  plants  the  cooling  tower  is  the 
preferred  method  of  providing  a  supply  of  condensing  water.     Cooling- 
towers  are  divided  into  two  classes,  known  as  natural  draft  and  mechanical 
draft  towers,  according  as  to  whether  the  air  is  drawn  through  the  tower 
by  a  chimney-like  action,  or  forced  into  the  tower  by  means  of  a  fan  or 
other  form  of  mechanical  impeller.     In  theory,  the  action  of  the  cooling 
tower  is  as  follows :  the  water  coming  from  the  condensers,  which  usually 
has  a  temperature  of  approximately  100°,  is  introduced  at  the  top  of  the 
tower,  which  is  filled  either  with  wooden  or  tile  checker  work  or  heavy 
galvanized, iron  wire  partitions.     As  the  water  descends  through  the  tower, 
flowing  over  the  checker  work  or  wire  mesh,  it  exposes  a  large  area  to 
the  action  of  the  air  which  is  flowing  upward  through  the  tower.     The 
air  entering  the  tower  has  the  temperature  and  humidity  of  the  outdoor 
air.     As  it  ascends  through  the  tower,  coming  into  contact  with  warm 
water,  it  chills  this  water  by  the  evaporation  of  a  small  portion  of  it, 
and  finally  leaves  the  top  of  the  tower  at  almost  the  temperature  of  the 


ART.  273  CAPACITY  OF  A  COOLING  TOWER  269 

entering  water  and  laden  almost  to  the  saturation  point  with  moisture. 
Since  it  is  warmed  as  it  ascends  through  the  tower,  it  expands  in  volume 
and  consequently  is  able  to  hold  more  moisture  than  it  would  were  it 
not  for  this  expansion.  The  addition  of  the  water  vapor  which  it  absorbs 
also  increases  the  volume.  A  portion  of  the  heat  taken  from  the  water 
is  carried  away  in  the  form  of  sensible  heat  in  the  air,  on  account  of  its 
rise  in  temperature.  The  most  of  it,  however,  is  carried  away  in  the  form 
of  latent  heat,  on  account  of  the  evaporation  of  a  portion  of  the  water. 
The  following  problem  will  serve  to  make  clear  the  action  of  such  a 
cooling  tower. 

273.  Capacity  of  a  Cooling  Tower.  Assume  that  a  cubic  foot  of  air 
enters  the  tower  at  a  temperature  of  70°  and  a  humidity  of  70  per  cent. 
Were  this  air  saturated  with  moisture,  we  find  from  the  steam  tables  that 
the  pressure  of  the  water  vapor  present  would  be  0.36  pounds  per  square 
inch.  The  actual  pressure  of  the  water  vapor  will  be  70  per  cent  of  this 
or  0.25  pounds  per  square  inch.  The  pressure  of  the  dry  air  is  therefore 
14.70  —  0.25=14.45  pounds  per  square  inch.  The  quantity  of  moisture 
contained  in  the  air  is  0.001148X0.70  =  0.000804  pounds  per  cubic  foot. 
From  the  equation  PV=XR  T  we  find  the  weight  of  one  cubic  foot  of 
dry  air  to  be 

14.45X144 
533X630  = 

The  total  heat  of  the  moisture  contained  in  the  air  is  found  by  adding  the 
heat  of  superheat  to  the  total  heat  at  the  temperature  corresponding 
to  the  pressure  of  the  water  vapor.  Since  the  superheat  is  11°,  the  specific 
heat  of  superheated  steam  of  this  temperature  is  0.46,  the  total  heat  is 
1085.4  B.T.U.  per  pound  and  the  weight  of  moisture  in  the  cubic  foot  of 
air  is  0.000804,  we  will  have  for  the  total  heat  of  the  moisture  in  1  cubic 
foot  of  air,  the  value 

.000804  (11X0.46+ 1085.4)  =0.876  B.T.U. 

Let  us  assume  further  that  the  air  comes  from  the  cooling  tower  at  a 
temperature  of  100°  and  saturated  with  moisture.  The  pressure  of  the 
moisture  contained  in  the  air  is  now  0.946  pounds  per  square  inch,  which 
leaves  as  the  pressure  of  the  dry  air  13.753  Ibs.  per  square  inch.  The  volume 
of  what  was  1  cubic  foot  of  air  will  now  be  increased,  the  new  volume 
being  to  the  old  volume  inversely  as  the  absolute  pressure  of  the  dry  air 
and  directly  as  its  absolute  temperature.  We  therefore  have  for  the  new 
volume  of  this  quantity  of  air 

14.45     560 


270  WATER-COOLING  APPARATUS  ART.  274 

This  quantity  of  air  will  contain  0.002851  X  1.11  =  0.00316  pounds  of  water- 
vapor  at  a  temperature  of  100°  when  saturated,  and  the  total  heat  of  this 
vapor  will  be  1103.6X0.00316  =  3.49  B.T.U.  It  will  be  seen  that  the 
amount  of  heat  carried  away  in  the  water  vapor  is  equal  to  3.49  —  0.88  =  3.61 
B.T.U.  for  each  cubic  foot  of  air  introduced  in  the  tower.  The  air  itself 
was  heated  from  a  temperature  of  70°  to  a  temperature  of  100°,  and  this 
30°  rise  in  temperature  added  to  it  0.0737X30X0.238  =  0.525  B.T.U., 
a  quantity  found  by  multiplying  the  weight  of  the  air  by  its  rise  in  tem- 
perature and  the  product  by  the  specific  heat  of  the  air  at  constant 
pressure.  The  total  quantity  of  heat  carried  away  by  each  cubic  foot 
of  the  air  introduced  into  the  tower  is  then  0.520  +  2.61  =  3.14  B.T.U. 

When  a  cooling  tower  is  working  at  approximately  its  rated  capacity 
the  water  will  be  cooled  until  its  temperature  is  about  that  of  saturated 
water  vapor  having  a  pressure  from  0.15  to  0.25  pounds  per  square  inch 
higher  than  that  of  the  water  vapor  in  the  entering  air.  The  air  will  leave 
the  tower  with  a  temperature  from  five  to  ten  degrees  lower  than  the 
entering  water  and  with  a  humidity  of  from  90  to  100  per  cent.  We 
are  usually  safe  therefore  in  assuming  that  each  cubic  foot  of  air  delivered 
to  the  tower  will  carry  away  at  least  2.5  B.T.U.  from  the  condensing 
water.  Since  a  condensing  steam  plant  of  good  economy  will  reject 
from  10,000  to  15,000  B.T.U.  per  horse-power  per  hour,  it  will  be  seen  that 
we  must  supply  to  the  cooling  tower  from  60  to  100  feet  of  air  per  minute 
for  each  horse-power  developed  by  the  plant. 

274.  Method  of  Designing  a  Cooling  Tower.  In  designing  a  cooling 
tower  it  is  necessary  to  provide  a  sufficient  surface  of  checkerwork  to 
evaporate  the  required  quantity  of  water;  to  provide  a  sufficient  cross- 
section  in  the  air  passages  so  that  the  pressure  required  to  circulate  the 
air  through  the  tower  will  not  be  excessive;  to  arrange  the  water  distribu- 
tion system  so  that  the  water  will  be  distributed  evenly;  to  arrange  the 
air  passages  so  that  the  supply  of  air  will  be  distributed  uniformly  to  all 
parts  of  the  checkerwork;  and  to  provide  means  for  moving  the  air  and 
pumping  the  water.  In  case  the  distribution  of  water  or  air  is  uneven, 
the  efficiency  and  capacity  of  the  tower  will  be  seriously  impaired. 

The  first  point  to  be  determined  in  cooling  tower  design  is  the  area 
of  checker  work  which  must  be  exposed  to  the  action  of  the  air.  The 
rate  of  evaporation  from  the  surface  of  checker  work  in  a  cooling  tower 
having  forced  draft  is  about  five  times  that  which  occurs  in  the  case  of 
an  open  pond  exposed  to  still  air.  The  rate  of  evaporation  per  square 
foot  of  surface  per  hour  will  therefore  be  found  by  multiplying  the  difference 
between  saturated  water  vapor  of  the  temperature  of  the  water  leaving 
the  tower  and  the  actual  pressure  of  the  water  vapor  in  the  air  entering 
the  tower  by  1.5.  Having  found  the  rate  of  evaporation  and  knowing 
the  temperature  of  the  water  entering  the  tower,  we  may  compute  by  the 


ART.  275    EXAMPLE  OF  THE  DESIGN  OF  A  COOLING  TOWER  271 

converse  process,  the  approximate  temperature  and  humidity  of  the  air 
leaving  the  tower,  and  from  this  we  may  determine  the  quantity  of  heat 
and  of  moisture  carried  off  per  cubic  foot  of  air  supplied.  From  the 
total  heat  rejected  by  the  engine  when  working  at  its  rated  load,  we  may 
determine  the  total  quantity  of  air  required,  and  the  total  area  of  the 
checker  work.  The  depth  of  the  checker  work  will  depend  on  the  available 
draft  in  case  the  tower  is  a  natural  draft  tower  and  may  be  given  any 
reasonable  value  in  the  case  of  a  forced  draft  tower.  It  is  usual  to  make 
the  depth  of  checker  work  in  the  latter  case  twice  the  least  dimensions 
of  the  base  of  the  tower. 

275.  Example  of  the  Design  of  a  Cooling  Tower.  We  will  assume  the  following 
problem  to  illustrate  the  method  of  cooling  tower  design.  Temperature  of  the  air 
entering  75°,  humidity  70  per  cent,  required  temperature  of  condensing  water  80°, 
temperature  of  water  entering  the  cooling  tower  110°.  The  pressure  of  water  vapor 
of  80°  temperature  is  0.505  pounds  per  square  inch.  The  pressure  of  the  water  vapor 
in  the  air  is  0.428X0.70=0.30  pounds  per  square  inch.  The  pressure  difference  is 
therefore  0.20  pounds  per  square  inch,  and  the  rate  of  evaporation  is  0.20X1.5=0.30 
pounds  per  square  foot.  The  pressure  corresponding  to  the  temperature  of  the  enter- 
ing water  is  1.27  pounds  per  square  inch.  Subtracting  the  0.20  pounds  difference  in 
pressure  to  maintain  the  computed  rate  of  evaporation  we  will  have  for  the  pressure 
of  the  water  vapor  in  the  air  discharged,  1.07  pounds  per  square  inch,  which  corre- 
sponds to  a  temperature  of  104°.  We  may,  in  practice,  assume  that  the  air  will  come 
from  the  tower  saturated  with  moisture  at  this  temperature  and  neglect  the  super- 
heat of  the  water  vapor  entering  the  tower.  The  weight  of  water  vapor  entering 
the  tower  per  cubic  foot  of  air  supplied  is  0.00135X0.70=0.00095  and  its  total  heat 
will  be  1094.3X0.00095  =  1.04  B.T.U.  The  pressure  of  the  dry  air  entering  the 
tower  will  be  14.70—0.30  =  14.40.  The  pressure  of  the  dry  air  leaving  the  tower 
will  be  14.70  -  1.07  =  13.63.  The  final  volume  of  the  air  will  be 

14.  40  .  .  460  +  104 

KeS*  460  +  75  =LllcU'ft- 

The  quantity  of  moisture  in  the  air  leaving  the  tower  will  be  1.11X0.00319=0.00353 
pounds  per  cubic  foot  of  air  supplied,  and  the  total  heat  will  be  0.000353X1033.4=3.64 
B.T.U.  The  amount  of  heat  carried  away  by  the  evaporation  of  the  moisture  will 
therefore  be  3.64  —  1.04  =  2.6  B.T.U.  per  cubic  foot  of  air  supplied.  The  air  itself  will 
be  increased  in  temperature  from  75°  to  104°,  and  the  sensible  heat  carried  away 
will  be  (since  a  cubic  foot  of  dry  air  weighs  approximately  0.075  pounds)  0.075X29 
X0.238=0.52  B.T.U.  The  heat  carried  away  per  cubic  foot  of  air  supplied  will 
then  be  0.52  +  2.6  =  3.12  B.T.U.  Assuming  that  the  engine  rejects  15,000  B.T.U. 
per  horse-power  per  hour,  we  will  then  have  for  the  required  air  supply, 


per  hour  or  80  cubic  feet  per  minute.  The  quantity  of  water  evaporated  by  each 
cubic  foot  of  air  supplied  is  0.00352—0.00095=0.00257  pounds.  Hence  the  quantity 
of  water  evaporated  per  horse-power  per  hour  will  be  4800X0.00257  =  12.4  pounds. 
We  have  already  determined  that  the  evaporation  per  square  foot  of  checker  work  will  be 


272 


WATER-COOLING  APPARATUS 


ART.  275 


0.30  pounds.     Consequently  the  number  square  feet  of  checker  work  required  per 
horse-power  will  be 


12.4 
0.30 


=  41. 


If  this  checker  work  be  assumed  to  consist,  as  it  often  does,  of  1-inch  cypress  planks 
laid  up  in  such  a  way  as  to  make  a  series  of  vertical  flues  4  inches  square,  as  shown 
in  Fig.  143,  we  will  have  an  evaporative  surface  of  7.7  square  feet  per  cubic  foot  of 
checker  work.  This  will  give  us  about  5.3  cubic  feet  of  checker  work  per  horse-power. 
In  the  case  of  a  1000  horse-power  cooling  tower  we  would  have  a  tower  14  feet  square 
with  a  depth  of  checker  work  of  about  28  feet. 

Under  these  circumstances,  the  net  area  of  the  air  passages  will  be  about  125 
square  feet,  and  since  the  total  quantity  of  air  required  is  80,000  cubic  feet  per  minute, 
the  velocity  of  the  air  in  the  passages  will  be  10.5  feet  per  second.  The  pressure  required 
to  produce  this  velocity  in  a  tower  of  this  height  is  about  the  pressure  produced  by  a 

column  of  water  f  inches  high.  The  resistance 
offered  by  such  a  tower  to  the  passage  of  the  air 
varies  directly  as  the  depth  of  the  checker  work 
and  as  the  1.8  power  of  the  velocity  of  the  air. 
Since  it  is  impracticable  in  the  case  of  a  natural- 
draft  tower,  to  obtain  by  means  of  the  difference 
in  density  of  the  air  within  and  without  the  tower 
a  difference  in  pressure  as  great  as  the  figure 
given,  a  natural-draft  tower  will  have  a  less 
depth  of  checker  work  and  a  much  larger  ground 
area  for  the  same  capacity.  In  general,  on  account 
of  the  lower  velocity  of  the  air,  the  rate  of  eva- 
poration in  a  natural-draft  tower  per  square 
foot  of  checker  y/ork  will  be  about  60  per  cent  of 
the  rate  in  a  forced-draft  tower,  consequently, 
about  If  times  as  much  evaporative  area  must  be 
provided  as  would  be  provided  in  the  case  of  a 
forced  draft  tower.  In  order  to  produce  th9  re- 
FIG.  143.— Arrangement  of  checker  quired  draftj  a  ghaft  or  chimney  extends  from  50 

to  100  feet  above  the  top  of  the  checker  work  on  a 
natural-draft  tower.   The  draft  which  such  a  tower 

will  produce  may  be  found  by  rinding  the  difference  in  weight  of  a  cubic  foot  of  external 

air  and  a  cubic  foot  of  the  air  coming  from  the  checker  work  and  multiplying  this 

by  the  vertical  distance  from  the  top  of  the  checker  work  to  the  top  of  the  tower. 

The  product  will  be  the  difference  in  pressure  in  pounds  per  square  foot,  which  may 

be  reduced  to  inches  of  water  by  multiplying  by  0.192. 

A  natural-draft  tower  of  the  same  capacity  as  the  one  we  have  just  designed  would 

have  8  cubic  feet  of  checker  work  per  horse-power,  or  8000  cubic  feet  altogether.     The 

weight  of  the  external  air  per  cubic  foot  will  be 


work  for  cooling  tower. 


14.40X144 


+  0.00093  =0.0740  Ibs. 


53.3X535 

The  weight  per  cubic  foot  of  the  air  in  the  shaft  will  be 
13.63X144 


53.3X564 


+  .003 19  =  .0687. 


PROBS.  1-11  PROBLEMS  273 

The  difference  in  density  will  be  0.0053,  and  the  draft  produced  will  be  0.001  inches 
of  water  per  foot  in  height  of  the  shaft. 

Assuming  the  same  depth  of  checker  work  as  in  the  forced-  draft  tower,  the  ground 
area  will  be  1.66  times,  and  the  air  velocity  only  0.60  times  the  former  value.  The 
resistance  of  the  checker  work  will  therefore  be  fX0.601-8=0.15  inches  of  water.  The 
height  of  tower  required  would  be  150  feet,  which  is  excessive.  Since  the  resistance 
of  the  tower  for  a  given  air  velocity  is  proportional  to  the  depth  of  checker  work, 
and  the  velocity  is  inversely  proportional  to  this  depth,  the  height  of  the  shaft  is 
proportional  to  the  2.8  power  of  the  depth  of  the  checker  work.  Assuming  a  reason 
able  height  of  shaft,  say,  60  feet,  we  will  have  for  the  depth  of  the  checker  work 


The  area  of  the  base  of  the  tower  will  then  be 

8000 


26 


=-286  sq.ft., 


or  the  tower  will  be  then  17  feet  square. 

The  volume  of  the  checker  work  and  the  draft  required  to  maintain  the  required 
air  velocity  varies  greatly  with  the  form  of  the  checker  work.  The  draft  needed  can 
be  computed  only  from  the  observed  performances  of  similar  towers.  In  forced  draft 
towers  the  power  required  by  the  fans  is  about  one  per  cent  of  the  power  of  the  station. 


PROBLEMS 

1.  It  is  desired  to  maintain  the  temperature  of  a  cooling  pond  at  75°.     The  mean 
summer  temperature  is  65°  and  the  humidity  50  per  cent.     It  is  used  in  connection 
with  a  200  horse-power  station  operating  12  hours  per  day,  using  18  Ibs.  of  water 
per  horse-power  per  hour.   Find  the  area  of  cooling  pond  required.      Ans.  21,8CO  sq.ft. 

2.  What  area  of  spray  pond  would  be  required  for  the  above  plant  ?    Ans.     600  ft. 

3.  One  cubic  foot  of  air  enters  a  cooling  tower  at  a  temperature  of  80°  and  a  hu- 
midity of  80  per  cent.     Find  the  total  heat  present  in  the  water  vapor,  disregarding 
the  superheat  of  the  vapor.  Ans.     1.375  B.T.U. 

4.  Within  the  tower  this  cubic  foot  of  air  is  raised  to  a  temperature  of  110°  and 
saturated  with  moisture.     Find  its  final  volume.  Ans.     1.122  cu.ft. 

5.  Find  the  total  heat  of  the  water  vapor  contained  in  this  air. 

Ans.  4.680  B.T.U. 

6.  Find  the  increase  in  the  sensible  heat  of  the  air.                      Ans.  0.52  B.T.U. 

7.  Find  the  heat  carried  away  per  cubic  foot  of  air  supplied.     Ans.  4.08  B.T.U. 

8.  Find  the  heat  carried  away  per  pound  of  water  evaporated. 

Ans.     1.370  B.T.U. 

9.  Water  comes  from  the  above  cooling  tower  at  a  temperature  of  95°.     What 
is  the  rate  of  evaporation  per  square  foot  of  checker  work,  assuming  forced  draft. 

Ans.     0.615  Ibs. 

10.  Find  the  number  of  square  feet  of  checker  work  required  for  a  power  plant  of 
1000  horse-power,  rejecting  12,000  B.T.U.  per  horse-power  hour.     Ans.      14,200  sq.ft. 

11.  How  many  cubic  feet  of  air  will  be  required  per  hour  by  the  above  plant? 

Ans.     2,940,OCO  cu.ft. 


CHAPTER  XVIII 


HOT  AIR  ENGINES 

276.  Characteristics  of  the  Hot  Air  Engine.  The  hot  air  engine  is 
a  heat  engine  which  uses  air  or  other  permanent  gas  as  a  working  fluid. 
Since  there  is  no  advantage  gained  by  employing  any  other  gas,  air  is 
the  working  fluid  invariably  chosen.  The  hot  air  engine  may  be  dis- 
tinguished from  the  internal  combustion  engine  by  the  manner  in  which 
the  working  fluid  is  heated,  namely  by  the  conduction  of  heat  from  some 
external  source  and  not  by  the  combustion  of  the  working  fluid  itself. 
It  is,  therefore,  unnecessary  for  the  hot  air  engine  to  reject  the  working- 
fluid  and  take  a  fresh  supply  at  the  completion  of  each  cycle,  as  is  done 
in  the  case  of  the  internal  combustion  engine.  The  hot  air  engine,  since 
the  advent  of  the  internal  combustion  engine,  is  not  of  great  commercial 
importance.  However,  several  of  these  engines  afford  excellent  illustra- 
tions of  important  principles  which  are  of  great  interest  in  connection 

with  the  probable  development  of 
internal  combustion  engines  and 
refrigeration  machinery,  and  are 
therefore  worthy  of  careful  study. 

277.  The  Carnot  Air  Engine. 
The  most  efficient,  and  in  theory 
the  simplest  cycle  which  may  be 
performed  by  the  working  fluid  of 
a  hot  air  engine,  is  the  Carnot  cycle. 
The  Carnot  cycle  has  never  been 
used  in  any  practical  engine  for  the 
reason  that  the  cylinder  volume  and 
the  pressure  range  required  in  order 
to  produce  a  very  moderate  amount 
of  power,  are  very  great.  This  may 
be  seen  by  reference  to  Fig.  144, 
which  shows  to  scale  the  Watt  dia- 
gram of  the  Carnot  cycle  for  air  for 
the  temperature  range  from  70°  to  cSOO°  F.  It  will  be  noted  that  the 


FIG.  144.— Theoretical  card,  to  scale,  from 
a  Carnot  cycle  air  engine. 


card    is    extremely    "  thin,3 


although    the  pressure  range  is  very  large. 

274 


ART.  277  THE  CARNOT  AIR  ENGINE  275 

This   is   a  condition   of   affairs  which   makes  for   very   low   mechanical 
efficiency  and  multiplies  greatly  the  practical  difficulties  of  operation. 

Assume  that  the  Carnot  cycle  engine  whose  Watt  diagram  is  illus- 
trated in  Fig.  144  uses  1  pound  of  air  for  its  working  fluid  at  an  initial 
temperature  (Tc)  of  530°  absolute,  an  initial  pressure  (Pc)  of  2000  pounds 
per  square  foot  (i.e.,  13.9  pounds  per  square  inch)  and  an  initial  volume 
(Vc)  of 

T7       WRTC       1X53.3X530 

Vc  =    --  --       -  14.2  cu.ft. 


Assume  that  this  air  is  compressed  isothermally  until  its  volume  at  d 
(Vd)  is  7.1  cubic  feet  and  its  pressure  (Pd)  is  4000  pounds  per  square  foot. 
Next,  the  air  will  be  compressed  adiabatically  from  d  to  a,  until  its  tem- 
perature (Ta)  is  1060°  absolute.  The  pressure  (Pa)  will  be 


__ 

T  \  r—  i  /1f)fiO\  -4 

Pa  =  Pd?          -  4000  =  45,000  Ibs.  per  sq.ft. 


\ 

The  volume  of  the  air  will  of  course  be 


The  gas  will  now  expand,  the  ratio  of  isothermal  expansion  being  the 
same  as  the  ratio  of  isothermal  compression,  namely  two  to  one,  and  the 
volume  and  pressure  at  b  will  become  2.52  cubic  feet  and  22,700  pounds 
per  square  foot,  respectively.  The  efficiency  of  the  cycle  is 

ya-yc_  1060  -530 
Ta  1060 

which  is  about  the  theoretical  efficiency  of  the  internal  combustion  engine 
cycles  usually  employed.  The  net  work  done  during  the  cycle  is  50  per 
cent  of  the  mechanical  equivalent  of  the  heat  supplied  during  isothermal 
expansion,  and  is  JPi  Vi  loge  r  =  iX45,OOOX  1.26Xloge  2-39,200  ft.  Ibs. 
Dividing  this  by  the  swept  volume,  which  is  Vv,—  Va  or  12.9  cubic  feet, 
we  will  have  3040  pounds  per  square  foot  for  the  mean  effective  pressure. 
It  will  be  seen  from  the  above  computations  that  the  maximum  pres- 
sure is  320  pounds  per  square  inch,  while  the  mean  pressure  is  only  20 
pounds  per  square  inch,  or  less  than  y15  of  the  maximum  pressure.  In 
the  case  of  the  steam  engine,  it  is  very  seldom  that  the  mean  effective 
pressure  falls  below  one-half  or  one-third  of  the  maximum  pressure. 
Since  the  friction  loss  in  an  engine  of  a  given  power  is  approximately  pro- 
portional to  the  ratio  of  the  maximum  to  the  mean  pressure,  it  may  be  seen 
that  the  friction  loss  in  the  case  of  a  Carnot  cycle  hot  air  engine  is  from 


276 


HOT  AIR  ENGINES 


ART.  278 


I- 


five  to  eight  times  that  of  a  steam  engine  of  equal  indicated  power.     Owing 

to  this  fact,  no  hot  air  engine    operating   on    the  Carnot  cycle  or  any 

approximation  to  it  has  ever  been  successfully  used. 

278.  The  Joule  Hot  Air  Engine.     The  simplest  of  the  practical  cycles 

employing  hot  air  as  the  working  fluid  is  the  Joule  cycle.     The  operation 

of  the  Joule  cycle  may  be  un- 
derstood by  reference  to  Fi'g. 
145.  In  cylinder  A,  a  quan- 
tity of  air  is  compressed 
adiabatically  to  some  high 
pressure  and  is  then  dis- 
charged at  constant  pressure 
into  the  heater  chamber  B. 
Cylinder  C  takes  the  same 
mass  of  air  from  the  heater 
chamber  and  expands  it  down 
to  its  original  pressure.  The 
volume  of  the  heating  and 
cooling  chambers  is  so  great 
that  no  sensible  variation  in. 
pressure  occurs.  After  ex- 


FIG.  145.— Diagram  of  a  Joule  cycle  air  engine.       pansion,  the  gas  is  rejected  to 

the  cooling  chamber  d  at  con- 
stant pressure.  Here  its  temperature  is  reducc-d  to  the  initial  temperature 
and  it  again  enters  cylinder  A  to  repeat  the  cycle.  It  is  not  necessary 
that  a  cooling  chamber  be  provided,  as  the  working  fluid  may  be  rejected  to 
the  atmosphere  and  a  fresh  quantity  taken  from  the  atmosphere  by 


u  g  i  h 

FIG.  146. — Watt  diagram  from  a  Joule  cycle  engine. 

cylinder  A.  The  equivalent  series  of  processes  consist  of  first,  compres- 
sion at  constant  pressure,  second,  adiabatic  compression;  third,  expan- 
sion at  constant  pressure;  fourth,  adiabatic  expansion.  The  Watt  diagram 
is  illustrated  in  Fig.  146.  Assume  that  the  temperature  of  the  air  in 


ART.  278  THE  JOULE  HOT  AIR  ENGINE  277 

the  heater  chamber  is  1200°  absolute  (740°  F.)  and  the  temperature  of  the 
atmosphere  530°  absolute  (70°  F.),  that  the  pressure  in  the  heater  chamber 
is  150  pounds  absolute,  per  square  inch,  and  that  one  pound  of  air  is 
introduced  into  and  withdrawn  from  the  heater,  per  cycle.  The  temper- 
ature of  compression  (at  a)  may  be  found  by  the  formula; 

r-i 


or 

71.^0  \ 

=  1030°, 


150  \ 
14.7/  ~ 


which  is  the  temperature  of  the  air  entering  the  heater  chamber.     The 
work  of  compression  in  cylinder  A  may  be  obtained  by  the  formula: 


U=n-  -  53.3  -_  =  6 

The  work  required  to  deliver  the  air  from  cylinder  A  into  the  heating 
chamber  will  be  RT,  which  becomes  53.3  X  1030-=  54,900  foot-pounds  (area 
g  a  f  o).     The  heat  imparted  to  the  air  in  raising  its  temperature  from 
1030°  to  1200°  at  constant  pressure  is 


which  is  185.5X170  =  31,700  foot-pounds.  The  work  done  by  the  air 
while  entering  the  cylinder  C  is  equal  to  53.3X1200  =  64,000  foot-pounds. 
(area  fbio)  The  air  is  expanded  from  a  pressure  of  150  pounds  absolute 
and  an  initial  temperature  of  1200°  to  a  pressure  of  14.7,  and  its  final 
temperature  is  therefore 


286 

=618° 


The   work  of  expansion  will  be 

77500  ft.lb, 


(area  b  c  j  i)  .  The  work  done  by  the  air  in  entering  cylinder  A  from  the 
cooler  is  53.3X530  =  28,300  foot-pounds  (area  e  d  h  o).  The  work  done 
in  expelling  the  air  from  cylinder  C  is  53.3X618  =  33,000  foot-pounds 
(area  ecjo).  The  heat  rejected  in  the  cooling  chamber  will  be 

(618-  530)  X  186.5  =16,400  ft.lbs. 


278 


HOT  AIR  ENGINES 


ART.  279 


The  quantity  of  work  done  is  the  difference  between  the  work  done  upon 
the  air  in  compressing  it  and  delivering  it  to  the  heater  and  rejecting  it 
to  the  cooler  and  that  done  by  the  air  in  entering  the  cylinders  and  expand- 
ing in  cylinder  C,  and  is  15,300  foot-pounds  (area  abed).  Dividing  this 
by  the  mechanical  equivalent  of  the  heat  imparted  to  the  pound  of  air 
in  the  heater,  we  will  have  for  the  efficiency  of  the  engine  48.2  per  cent. 
An  inspection  of  the  above  work  will  show  that  the  heat  supplied  is 
proportional  to  Tb—  Taj  the  heat  rejected  to  Tc—Td,  and  the  work  done 
to  (Tb-Ta)-(Tc-Td).  The  efficiency  of  the  Joule  cycle  is  therefore 
given  by  the  expression 

frr      i    rri          nn         nn 
lb+  J  d~  lg  —  ic 

7\ T  y 

*  b       *  a 

in  which  Tb  =  the  temperature  of  the  air  leaving  the  heater,  7^  =  the 
temperature  of  the  air  entering  the  heater,  7^  =  the  temperature  of  the 
air  entering  the  cooler,  or  rejected  from  the  engine,  Td  =  the  temperature 
of  the  air  leaving  the  cooler,  or  taken  into  the  engine. 

279.  The  Stirling  Hot  Air  Engine.  The  Stirling  engine  utilizes  the 
regenerator  principle  in  order  to  attain  the  efficiency  of  the  Carnot  cycle 
without  the  accompanying  mechanical  disadvantages.  The  theory  of 
this  engine  will  be  best  understood  by  reference  to  Fig.  147  although 

[the  parts  of  the  engine,  in 
practice,  are  arranged  in  an 
entirely  different  manner.  In 
the  figure,  A  is  a  piston  which 
works  within  the  large  cylin- 
der By  C  is  a  piston  which 
works  within  the  small  cylin- 
der Z),  which  is  connected  with 
the  large  cylinder  by  the  pas- 
sage F.  Assume  that  both 
pistons  are  at  the  lowest  point 
of  their  stroke,  as  shown  in  the 
illustration.  If  piston  A  now 
be  caused  to  rise,  it  will  trans- 
fer the  air  above  it  from  its 
upper  to  its  under  side,  causing 
it  to  flow  through  the  regen- 
erator, marked  R,  which  may 
FIG.  147.— Diagram  of  a  Stirling  air  engine.  consist  of  a  large  quantity  of 

wire    gauze.      The   air  above 

the  piston  A  is  exposed  to  the  action  of  a  cooler,  as  shown,  and  is  therefore 
at  the  temperature  of  the  cooler,  Tc.  The  air  below  the  piston  A  is  exposed 


Cooler 


Heater 


ART.  279 


THE  STIRLING  HOT  AIR   ENGINE 


279 


to  the  fire,  or  to  some  other  source  of  heat,  and  is  therefore  at  the  tem- 
perature of  the  heater,  71/.  In  passing  through  the  regenerator,  the  tem- 
perature of  the  air  will  be  raised  from  the  temperature  of  the  cooler  to 
the  temperature  of  the  heater,  by  the  regenerative  action.  As  a  result  of 
this  transfer  and  increase  in  temperature  of  the  air,  its  pressure  will 
rise.  When  piston  A  has  reached  the  top  of  its  stroke,  the  pressure  of 
the  air  will  have  risen  from  its  original  value  Pc,  to  the  value  Pf.  Piston 
C  is  now  permitted  to  rise,  the  air  expanding  isothermally,  absorbing 
heat  and  performing  work  during  the  process.  Piston  C  having  reached 
the  top  of  its  stroke,  piston  A  is  now  depressed,  forcing  the  air  below  it 
through  the  regenerator  and  past  the  cooler  into  the  upper  part  of  B.  As 
it  passes  through  the  regenerator,  the  air  is  cooled  from  the  temperature 
of  the  heater  to  the  temperature  of  the  cooler.  Piston  C  is  now  forced 
downward,  isothermally  compressing  the  air,  while  it  rejects  heat  to  the 
cooler.  No  work  is  done  by  or  upon  piston  B}  and  the  net  work  of  the 
cycle  is  the  difference  between  the  work  performed  upon  piston  D  during 
its  upward  stroke,  and  by  it  during  its  downward  stroke. 

The  efficiency  of  a  Stirling  engine  is  in  theory  the  same  as  the  efficiency 
of  a  Carnot  cycle  engine.  In  practice,  of  course,  it  is  necessary  that  there 
be  a  considerable  tempera- 
ture difference  between  the 
heater  and  the  air  under 
the  transfer  piston,  between 
the  cooler  and  the  air  above 
the  transfer  piston,  and 
between  any  point  in  the 
regenerator  and  the  air 
passing  that  point.  The 
card  given  by  the  working 
cylinder  of  the  engine  is 
shown  in  Fig.  148.  Line 
a  b  represents  the  expan- 
sion of  the  air  during  the 
rise  of  piston  C.  Line  b  c 
represents  the  fall  in  pressure  of  the  air  at  constant  volume  (i.e.,  while  the 
piston  C  is  at  the  top  of  its  stroke)  on  account  of  its  transfer  by  piston  A. 
Line  c  d  represents  the  compression  of  the  air  while  piston  C  descends. 
Line  d  a  represents  the  rise  in  pressure  at  constant  volume,  while  the 
transfer  piston  is  transferring  the  air  from  the  upper  to  the  lower  side. 

Assuming  that  1  pound  of  air  having  a  pressure  of  100  pounds  per  square  inch 
absolute  at  point  d,  is  used  as  the  working  fluid,  that  the  ratio  of  isothermal  expansion 
is  2,  that  the  temperature  of  the  air  above  the  transfer  piston  is  70°  F.,  and  that  below 
the  transfer  system  piston  740°  F.,  and  neglecting  the  volume  of  the  regenerator 


FIG.  148. — Watt  diagram  from  a  Stirling  engine. 


280  HOT  AIR  ENGINES  ART.  279 

spaces  and  air  passages,  we  will  obtain  the  following  results  from  the  Stirling  cycle. 
During  the  rise  of  the  transfer  piston,  no  work  will  be  done  or  absorbed,  the  tem- 
perature of  the  air  will  rise  from  530°  absolute  to  1200°  absolute  and  the  pressure 
will  rise  from  100  to  226.5  pounds  per  square  inch.  The  air  is  heated  by  heat  stored 
in  the  regenerator,  and  during  this  portion  of  the  cycle  it  receives  no  heat  from  the  heater. 
During  the  rise  of  piston  D,  the  air  expands  isothermally,  receiving  heat  from  the  heater 
in  order  to  maintain  its  temperature  constant.  The  amount  of  heat  so  received  is  equal 
to  the  amount  of  work  done  by  the  air  upon  piston  C,  which  is  53.34X1200Xloge2  = 
44,350  foot-pounds.  This  is  the  mechanical  equivalent  of  the  heat  received  by  the 
air  from  the  heater,  during  this  portion  of  the  cycle,  and  is  represented  by  the  area 
a  b  ef.  At  the  end  of  isothermal  expansion,  the  pressure  of  the  air  has  fallen  to 
113.25  pounds  per  square  inch.  During  the  descent  of  the  transfer  piston,  a  part  of 
the  air  is  transferred  through  the  regenerator,  and  its  temperature  falls  to  that 
of  the  cooler.  No  work  is  done  or  absorbed  during  this  portion  of  the  cycle  and  no 
heat  is  taken  from  the  heater  or  imparted  to  the  cooler.  Since  the  ratio  of  expansion 
is  2  to  1,  the  volumes  of  the  transfer  cylinder  and  the  working  cylinders  are  equal 
and  are  each 

530X53.34 


Hence  after  the  transfer  of  part  of  the  air  to  the  upper  side  of  piston  B  has  been 
effected  we  will  have  1.964  cubic  feet  of  air  at  a  temperature  of  530°  and  1.964  cubic 
feet  at  a  temperature  of  1200°.  Since  the  pressures  and  the  volumes  are  the  same 
in  each  case,  the  masses  will  be  inversely  proportional  to  the  absolute  temperatures, 
and  the  quantity  in  the  transfer  cylinder  will  be 

1200         0.694  Ibs. 


1200+530 
The  pressure  of  this  air  (Pc)  will  be 


0.694X53.34X530 

~  ~    =  per  square        ' 


During  the  descent  of  piston  D,  the  remainder  of  the  air  which  is  contained  in 
cylinder  C,  is  transferred  through  the  regenerator  and  the  cooler  to  the  upper  s'de 
of  the  transfer  piston,  and  the  whole  quantity  of  air  is  compressed.  That  portion 
of  the  air  within  cylinder  C  which  is  continually  diminishing  in  quantity  rejects  to 
the  heater  the  heat  equivalent  of  the  work  performed  in  compressing  it.  The  air  in 
the  transfer  cylinder,  which  is  continually  increasing  in  quantity,  rejects  to  the  cooler 
the  heat  equivalent  of  the  work  spent  in  compressing  it.  In  order  to  find  the  amount 
of  work  done  during  the  compression,  we  must  determine  the  relation  between  the 
pressure  and  volume  on  the  whole  mass  of  gas  contained  in  the  engine  during  the 
descent  of  the  working  piston.  Let  V  be  the  volume  of  the  working  cylinder.  Then 
the  mass  of  the  air  in  the  working  cylinder,  Wl}  will  be  to  the  mass  of  the  air  in  the 
transfer  cylinder,  TF2,  directly  as  the  volume  of  the  air  in  the  working  cylinder  is  to 
that  in  the  transfer  cylinder  and  inversely  as  the  temperature  of  the  air  in  the  work- 
ing cylinder  is  to  that  in  the  transfer  cylinder.  Consequently,  we  may  write 

=  530  V 

1      530  V  +  1200  XI.  966* 


ART.  279  THE  STIRLING  HOT  AIR  ENGINE  281 

The  pressure  of  this  mass  may  be  obtained  from  the  formula  PV^W^^RT  and  will  be 

53.34X1200X530^  63,900 
530  F  + 2360       ~  F  +  445' 

The  work  done  upon  the  gas  will  therefore  be 

rvd  ri.966      JY 

I     V  rfF=63,900  (  -^  — . 

JVC  Jo          F  +  4.45 

Integrating,  we  obtain 

63,900  loge  |^i|j  =  23,400  ft.-lbs. 

Subtracting  this  from  44,350  foot-pounds  the  work  done  by  the  gas  during  the  rise 
of  the  working  piston,  we  will  have  20,950  foot-pounds  for  the  net  work  of  the  cycle. 
The  swept  volume  is  1.964  cubic  feet  and  the  mean  effective  pressure  is 

20,950 

=  74.0  Ibs.  per  square  inch. 


144X1.966 
The  ratio  of  the  maximum  to  the  mean  effective  pressure  is      T-TT,  or   about    3 


to  1,  a  condition  of  affairs  very  much  more  favorable  to  mechanical  efficiency  than  is 
the  case  when  the  Carnot  cycle  is  employed.  The  quantity  of  heat  rejected  to  the 
cooler  is  equal  to  the  work  done  in  compressing  the  variable  quantity  of  gas  contained 
above  the  transfer  piston  during  the  descent  of  the  working  piston.  Since  V  equals 
the  volume  of  gas  in  the  working  cylinder  during  this  period,  the  total  volume  of  the 
gas  will  be  V  +  1.966.  The  amount  of  work  done  during  any  small  portion  of  the  stroke 
of  the  working  piston  upon  the  two  quantities  of  gas  will  be  proportional  to  their  volumes 
at  that  instant.  Consequently,  by  multiplying  the  total  work  done  during  any  instant 
by  the  ratio  of  the  volume  of  the  transfer  cylinder  to  the  total  volume  of  the  gas  at 
that  instant  we  will  have  the  work  done  upon  the  gas  in  the  transfer  cylinder  during 
that  instant.  Multiplying  the  equation  for  the  work  performed  upon  the  gas  during 

1  966 

the  descent  of  the  working  piston  by  ^—^  -^^,  we  will  have 

V    i*  J-  .t.'UO 


This  may  be  written 


Integrating  this,  we  will  have 

.416-41. 1-4X8.74\  1.966 

0 


125  600  (  1  \ 

25'6°°  \41.10  -4  X8.74J 


Solving  this  we  will  have  for  the  mechanical  equivalent  of  the  heat  rejected  to 
the  cooler  16,540  foot-pounds.  Subtracting  this  quantity  from  the  total  work  done 
upon  the  gas  in  compressing  it  we  will  have  the  mechanical  equivalent  of  the  heat 
restored  to  the  heater,  which  is  6,860  foot-pounds.  In  order  to  obtain  the  efficiency 
of  the  cycle,  we  must  divide  the  net  work  of  the  cycle  by  the  net  heat  supplied,  which 


HOT  AIR  ENGINES  ART.  280 

is  equal  to  the  heat  supplied  during  isothermal  expansion  less  the  heat  restored  to 
the  heater  during  compression,  and  we  will  obtain 

20,950 


44,350-  6860 

It  will  be  noted  that  the  cycle  is  composed  exclusively  of  reversible  processes,  and 
the  efficiency  of  the  cycle  is  in  consequence  that  of  the  Carnot  engine,  and  is,  for  the 
case  chosen, 

1200-530 


which  is  the  same  as  was  obtained  by  computation  of   the  work  performed,  and  the 
heat  supplied  and  rejected. 

Had  the  working  cylinder  been  connected  with  the  upper  end  of  the  transfer 
cylinder  the  cycle  would  have  differed  from  that  described,  in  that  during  the  descent 
of  the  working  piston  the  compression  would  have  been  isothermal,  and  during  the 
rise  of  the  working  piston,  heat  would  have  been  absorbed  from  both  the  heater  and 
the  cooler.  The  efficiency  of  the  cycle  would  l>e  exactly  the  same  as  before. 

In  practice,  the  Stirling  engine  is  subject  to  several  losses,  and  the 
card  given  by  the  engine  is  not  exactly  of  the  form  computed,  since  the 
regenerator  and  the  connecting  passages  have  some  volume.  Neither 
is  the  action  of  the  regenerator  a  perfectly  reversible  process  in  practice. 
Usually,  the  temperature  difference  between  the  air  entering  and  that 
coming  from  the  cool  end  of  the  regenerator  is  from  5  to  20  per  cent  of 
the  difference  in  temperature  of  the  two  ends  of  the  regenerator.  On 
this  account,  the  actual  efficiency  of  the  Stirling  engine  is  only  about 
60  per  cent  of  its  theoretical  efficiency.  In  addition,  there  are  practical 
difficulties  encountered  in  its  use,  which  may,  however,  be  overcome  by 
the  use  of  proper  materials.  Modifications  of  the  Stirling  cycle  will 
probably  serve  as  a  basis  for  future  improvements  in  the  internal  com- 
bustion engine,  since  this  engine  is  in  theory  the  most  efficient  one  which 
has  ever  been  practically  successful. 

280.  The  Ericsson  Hot  Air  Engine.  The  principle  of  the  Ericsson 
hot  air  engine  is  shown  in  Fig.  149.  This  engine  is  usually  built  only 
in  small  sizes  and  used  for  pumping  water.  The  method  of  operation 
is  as  follows:  Within  the  cylinder  A  is  a  gas-tight  piston  B,  termed  the 
working  piston.  Through  a  stuffing-box  in  this  piston  there  passes  a 
rod  which  operates  the  loose-fitting  plunger,  C.  The  purpose  of  this 
plunger  is  to  transfer  the  air  from  the  lower  to  the  upper  end  of  the 
cylinder  and  back  again,  and  it  is  therefore  termed  the  transfer  plunger. 
Both  piston  and  plunger  being  at  the  top  of  the  stroke,  as  is  shown  in 
Fig.  149,  the  plunger  descends,  transferring  the  air  from  the  furnace  at 
the  bottom  to  the  comparatively  cool  region  at  the  top.  In  its  passage 


ART.  280 


THE  ERICSSON  HOT  AIR  ENGINE 


283 


the  air  flows  in  a  thin  sheet  over  the  water-cooled  surface  of  the  cylinder, 
and  its  heat  is  transferred  to  the  water  jacket.  The  air  being  cooled, 
its  pressure  is  reduced.  While  the  transfer  plunger  remains  at  the  bottom 
of  its  stroke,  the  working  piston  descends,  compressing  the  air  con- 
tained in  the  cylinder.  The  transfer  plunger  now  rises  while  the  piston 
remains  stationary,  transferring  the  air  to  the  lower  end  of  the  cylinder, 
where  it  is  heated,  with  resulting  increase  of  pressure.  The  piston  now 
rises  as  a  result  of  the  increase  in  pressure  and  performs  work. 

Since  this  engine  lacks  a  regenerator,  it  is. less  efficient  than  the  Stirling 
engine.     Its  principal  merit  is  that  it  is  very. simple  and  unlikely  to  get 


FIG.  149. 


FIG.  150 


out  of  order.  In  practice,  the  piston  and  plunger  are  so  connected  to 
the  crank  of  the  engine  that  they  both  are  in  motion  continually,  instead 
of  each  one  stopping  while  the  other  is  performing  its  stroke.  This  is 
accomplished  by  the  mechanism  shown  in  Fig.  149,  the  piston  and 
water  pump  being  operated  by  the  walking-beam,  while  the  transfer 
plunger  is  operated  by  the  bell  crank.  It  will  be  seen  that  the  pmnger 
is  near  the  end  of  its  stroke  and  is  almost  motionless  while  the  piston  has 
its  maximum  velocity  and  is  at  the  middle  of  its  stroke.  The  form  of 
card  given  by  the  Ericsson  engine  is  shown  in  Fig.  150. 


284  HOT  AIR  ENGINES  PROBS.  1-11 


PROBLEMS 

1.  Find  the  diameter  and  length  of  stroke  which  would  theoretically  be  required 
by  an  engine  utilizing  the  Carnot  cycle  worked  out  in  Art.  277.     Assume  a  speed  of 
150  revolutions  per  minute,  that  the  length  of  stroke  is  1?  times  the  diameter,  that 
the  engine  is  100  horse-power  and  is  single  acting.  Ans.     22"X33". 

2.  Find  the  length  of  stroke  and  the  diameters  of  the  compression  and  working 
cylinders  of  an  engine  utilizing  the  Joule  cycle  worked  out  in  Art.  278.     The  engine 
is  of   100  horse-power  and  makes  150  revolutions  per  minute.     Assume  the  length 
of  stroke  to  be  equal  to  1^  times  the  diameter  of  the  compression  cylinder  and  that 
the  cylinders  are  single  acting.  Ans.     30.5" X  45.7"  and  32.9"  X  45.7". 

3.  A  Stirling  engine  operates  between  temperatures  of  200  and  1000°  F.     The 
pressure  when  both  pistons  are  in  their  lowest  positions  is  150  Ibs.  per  sq.in.      Find 
the  pressure  after  the  transfer  cylinder  is  raised.  Ans.     332  Ibs.  per  sq.in. 

4.  Assuming  1  Ib.  of  air  as  the  working  fluid  and  that  the  volume  of  the  transfer 
cylinder  is  twice  the  volume  of  the  working  cylinder,  find  the  work  of  isothermal 
expansion.  Ans.     31,550  ft.lbs. 

7.  Find  the  pressure  ta  the  end  of  isothe^^nal  expansion.     Ans.    221  Ib  per  sq.in. 

6.  Y'md  the  pressure  of  the  air  after  the  descent  of  the  transfer  piston. 

Ans.     122  Ibs.  per  sq.in. 

7.  Find  the  value  of  the  index  of   the  compression  curve,  assuming  that  it  follows 
the  law 

PVn  =  a  constant. 

Ans.     n=-51 

8.  Find  the  work  of  compression  on  the  same  assumption.        Ans.     16100  ft.lbs. 

9.  Find  the  net  work  of  the  cycle.  Ans.     15450  ft.lbs. 

10.  Find  the  net  work  per  cubic  foot  of  swept  volume  of  the  working  cylinder. 

Ans.     18,940  ft.lbs. 

11.  Find  the  size  of  working  cylinder  required  for  a  100  horse-power  engine,  oper- 
ating at  150  revolutions  per  minute,  utilizing  the  Stirling  cycle  just  developed.   Make 
the  stroke  1^  times  the  diameter  of  the  cylinder.  Ans.     11. 95"  X 17. 9". 


CHAPTER  XIX 


THE   INTERNAL  COMBUSTION  ENGINE 

281.  Characteristics  of  the  Internal  Combustion  Engine.     An  internal 
combustion  or  gas  engine  is  a  heat  engine  in  which  the  working  fluid 
consists  of  a  mixture  of  air  and  inflammable  gas  or  vapor,  the  combustion 
of  which  furnishes  the  heat  necessary  for  the  operation  of  the  mechanism. 
The  internal  combustion  engine  differs  from  all  other  heat  engines  in  that 
the  combustion  which  supplies  the  heat  occurs  within  the  working  cham- 
ber or  cylinder  of  the  engine  itself.     In  all  other  heat  engines,  the  working 
fluid  and  the  combustible  are  separate  substances,  and  the  working  fluid 
is  usually  heated  in  a  separate  chamber  from  that  in  which  it  performs 
its  work.     As  in  any  heat  engine,  the  working  fluid  of  the  internal  com- 
bustion engine  is  caused  to  perform  a  thermodynamic  cycle  whose  form 
is  determined  by  the  nature  of  the  fluid  and  the  arrangement  of  the  engine 
mechanism. 

282.  The  Otto  Cycle  Engine.     The  internal  combustion  engine  cycle 
which  is  in  most  common  use  is  usually  termed  the  -Otto  cycle,  and  was  first 
proposed  by  Beau  de  Rochas.     It  is  also  known  as  the  constant -volume 
cycle,  and  as  the  four-stroke  cycle.     The  operations  of  the  Otto  cycle  may 
be  understood  by  reference  to  Fig.  151.     The  engine  cylinder  is  an  iron 


FIG.  151. — Diagram  of  a  four-cycle  gas  engine. 

casting  A  provided  with  an  inlet  valve  I  and  an  exhaust  valve  E.  Within 
the  cylinder  moves  a  gas-tight  piston  which  is  often  made  of  the  form 
shown,  performing  at  the  same  time  the  functions  of  a  piston  and  of  a 
cross-head.  This  type  of  piston  is  known  as  a  trunk  piston.  As  the 

285 


286  THE  INTERNAL  COMBUSTION  ENGINE  ART.  283 

crank  revolves  in  the  direction  shown  by  the  arrow,  the  piston  is  moved 
back  and  forth.  Assume  that  the  engine  is  in  the  position  shown,  with 
the  crank  on  the  outer  center,  then  as  the  crank  revolves  it  will  begin 
to  force  the  piston  inward.  The  valve  E  being  held  open  by  the  mechanism  of 
the  engine  during  this  stroke,  the  contents  of  the  cylinder  will  be  expelled. 
This  first  stroke  is  therefore  termed  the  exhaust  stroke  of  the  cycle.  When 
the  piston  has  reached  the  end  of  its  exhaust  stroke,  the  valve  E  closes 
and  the  valve  /  opens.  The  piston  then  begins  to  move  forward,  and 
draws  in  a  quantity  of  air  with  which  is  mixed  a  combustible  gas.  This 
second  stroke  is  known  as  the  suction  stroke  of  the  cycle,  and  the  mixture 
drawn  into  the  cylinder  is  termed  the  charge.  When  the  piston  reaches 
the  end  of  this  stroke,  the  valve  /  also  closes,  and  the  crank  continuing 
to  revolve,  the  piston  is  again  forced  inward,  adiabatically  compressing 
the  charge  into  the  clearance  space  at  the  end  of  the  cylinder.  This  third 
stroke  is  known  as  the  compression  stroke.  The  volume  of  the  clearance 
space,  which  usually  ranges  from  12  per  cent  to  30  per  cent  of  the  swept 
volume  of  the  cylinder,  is  termed  the  clearance  volume.  When  the  pis- 
ton reaches  the  end  of  the  compression  stroke,  the  charge,  which  is  now 
highly  compressed  and  heated,  is  ignited,  usually  by  means  of  an  electric 
spark.  On  account  of  its  high  temperature  and  pressure  the  charge 
burns  almost  instantly,  and  the  heat  so  generated,  by  raising  the  tem- 
perature of  the  charge,  very  greatly  increases  its  pressure.  During  the 
fourth  stroke  of  the  piston  the  charge  expands  adiabatically.  Because 
of  the  great  pressure  resulting  from  its  explosion  much  more  work  will 
be  done  by  the  charge  during  this  stroke  than  was  done  upon  it  during 
the  compression  stroke.  The  fourth  stroke  is  therefore  known  as  the 
working  stroke  of  the  cycle.  When  the  piston  reaches  the  end  of  the 
working  stroke,  the  exhaust  valve  E  again  opens,  and  both  the  working- 
fluid  and  the  mechanism  of  the  engine  return  to  their  original  condition. 

It  will  be  seen  that  it  requires  four  strokes  of  the  engine  to  complete 
the  cycle.  During  the  first  or  exhaust  stroke  the  pressure  upon  the  piston 
is  only  slightly  above  that  of  the  atmosphere  and  during  the  second  or 
suction  stroke  only  slightly  below.  Although  the  amount  of  work  per- 
formed in  expelling  the  burned  charge  and  in  drawing  in  a  fresh  one 
varies  somewhat  with  the  speed  of  the  engine  and  the  size  of  the  valves 
and  gas  passages,  it  is  very  small  under  ordinary  conditions.  Hence  the 
suction  and  exhaust  strokes  need  not  be  considered  in  connection  with 
the  thermodynamic  cycle,  which  is  performed  during  the  compression 
and  working  strokes  only. 

283.  The  States  of  the  Working  Fluid  During  the  Otto  Cycle.  The 
pressure-volume  diagram  of  the  working  fluid  of  an  Otto  cycle  engine  is 
shown  in  Fig.  152.  The  horizontal  distance  Ocf  represents  the  clearance 
volume,  while  the  distance  c'a'  represents  the  swept  volume  of  the  cylin- 


ART.  283 


THE  STATES  OF  THE  WORKING  FLUID 


287 


der.  a  c  is  the  adiabatic  compression  line,  the  cylinder  containing  a 
charge  at  atmospheric  temperature  and  pressure  at  point  a.  At  point  c, 
the  charge  is  instantly  heated  at  constant  volume  by  the  explosion,  the 
pressure  rising  as  represented  by  line  ex.  Line  xt  is  the  adiabatic  expansion 
line  of  the  charge  and  the  line  t  a  represents  the  cooling  of  this  charge  at 
constant  volume  at  the  end  of  expansion.  The  computations  of  the 


a' 
FIG.  152. — Theoretical  card  from  an  Otto  cycle  engine. 

pressures,  temperatures,  and  so  on  of  the  -working  fluid  at  various  point K 
in  the  cycle  may  be  performed  as  follows: 

Let  Pa  =  the  absolute  pressure  of  the  atmosphere  in  pounds  per  square 
foot  ; 

Fa  =  the  swept  volume  +  VC  in  cubic  feet; 

Ta  =  the  absolute  temperature  of  the  atmosphere; 

Pc  =  the  absolute  pressure  of  compression  in  pounds  per  square  foot ; 

Fc  =  the  volume  of  the  compression  space  in  cubic  feet; 

Tc  =  the  absolute  temperature  of  compression ; 

Px  =  ihe  absolute  pressure  of  explosion; 

Vx=  Fc  =  the  volume  at  explosion; 

7^  =  the  absolute  temperature  of  explosion; 

P/  =  the  absolute  terminal  pressure  in  pounds  per  square  foot; 

Vt  =  Va  the  terminal  volume  in  cubic  feet  ; 

Tt  =  the  absolute  terminal  temperature ; 

Ha  =  the  heat  in  B.T.U.'s  added  at  explosion; 

Hr  =  the  heat  in  B.T.U.'s  rejected  at  exhaust; 

TF=the  weight  of  gas  contained  in  the  cylinder; 
Va  —  Vc  =  the  swept  volume  in  cubic  feet  =  Vt  —  Vx< 


288  THE  INTERNAL  COMBUSTION  ENGINE  ART.  283 

The  weight  of  the  charge  will  be 


The  volume  of  the  compression  space  will  be 

j_ 

v°=v«(jr)r (2) 

The  temperature  of  compression  will  be 


\*  c 

The  rise  in  temperature  resulting  from  the  explosion  will  be 

IT 

rp  rp     _  a  f  A\ 

^  Wc~' 

The  heat  added  as  a  result  of  the  explosion  will  be 

Ha=  WC.(T,-TC)      .......     (5) 

The  terminal  temperature  will  be 


T       T      V"\~l      T   (P'\' 

T*  T*-     ....... 


It  will  also  be 


rr,     m 

^a  J-  x  /7x 

—m  —  ,      .........      (7) 


since 

Tc:Ta::Tx:Tt (8) 

The  fall  in  temperature  at  the  end  of  expansion  will  be 

The  heat  rejected  will  be 

#r=  WCv(Tt-Ta) (10) 

The  efficiency  of  the  cycle  will  be 


or 

Cv(Tx-Tc)-Cv(Tt-Ta) 


ART.  283 


THE  STATES  OF  THE  WORKING  FLUID 


289 


Simplifying,  this  becomes 


E  =1- 


Tt-T 


T    —T  ' 

J-  x       1  c 

which  on  substituting  from  (7)  reduces  to 


(13) 


(14) 


It  appears  from  the  above  equation  that  the  higher  the  compression 
temperature  (or  pressure),  the  greater  the  efficiency  of  the  cycle,  and  that 
the  efficiency  is  theoretically  independent  of  the  explosion  and  terminal 
temperatures  and  pressures  and  of  the  amount  of  heat  added.  The 
relation  between  the  compression  pressure  and  the  efficiency  of  the  cycle 
may  be  seen  in  Fig.  153. 


w 


25  50  75  100  125  150          175          200 

Compression  Pressure  in  Lbs.  per  Sq.  In.  Gasre. 


FIG.  153. — Relation  between  the  efficiency  and  compression  pressure. 
The  work  of  compression  is 

PcVc-PaVa      R(Tc-Ta) 


Uac  = 
The  work  of  expansion  is 


P,Vc-PtVa      R(Tx-Tt} 


(15) 


(16) 


The  work  done  is  equal  to 

U  =  ^ 


(Px-Pc)Vc-(Pt-Pa)Vg 


.     •     (17) 


290  THE  INTERNAL  COMBUSTION  ENGINE  ART.  284 

Afef 

The  work  done  per  cubic  foot  of  swept  volume  is 

U 


Va-Vc' 
The  theoretical  horse-power  of  an  engine  employing  the  cycle  is 


d8) 


HP   -  -  (19) 

~  33,000  (Va-Ve)' 

in  which  N  is  the  number  of  cycles  (i.e.,  one-half  of  the  number  of  revolu- 
tions) per  minute. 

Also  for  convenience  in  computation,  it  may  be  noted  that 


(20) 


v 


and 

Px:Pe::Pt:Pa  ........     (21) 

The  compression  volume  is  generally  expressed  as  a  per  cent  of  the  swept 
volume  thus 

yc  (in  per  cent)  =    „  —  ~-  .......     .     (22) 

V  n  V   r. 


(I 


It  will  be  shown  in  the  next  chapter  that  the  actual  cycle  performed  in 
the  Otto  gas  engine  differs  slightly  from  the  theoretical  cycle.  The 
differences  are  not  so  great  as  they  are  in  the  case  of  steam  engine  cycles, 
however,  and  the  actual  card  has  very  nearly  the  form  of  the  theoretical 
card. 

284.  Example  Showing  the  Method  of  Computing  the  States  of  the  Working 
Fluid.  The  following  example  will  serve  to  show  the  method  of  computing  the  form 
of  the  theoretical  indicator  card,  the  work  done  and  the  efficiency  of  an  Otto  cycle. 
Assume  that  the  compression  pressure  is  140.  pounds  absolute  (i.e.,  about  125  pounds 
gage),  that  the  temperature  of  the  gases  after  explosion  will  be  3500°  absolute,  and 
that  the  temperature  of  the  mixture  entering  the  cylinder  is  70°  F.  The  compu- 
tations will  be  carried  out  for  1  pound  of  air.  The  initial  volume  is  obtained  from 
the  equation 

PV-WRT, 
and  is 


The  volume  of  the  compression  space  per  pound  of  air  will  be 

J_ 
Vc  =  13.32  (-^ \  "  =2.69cu.ft. 


ART.  284  EXAMPLE  OF  AN   OTTO  CYCLE  291 

The  swept  volume  per  pound  of  air  will  be 

13.32-2.69=10.63  cu.ft  ......     .     .     .     .     (3) 

The  temperature  of  compression  will  be 

(1  40  \  •  29 
—  ™j      =  1020°  absolute  ........     (4) 

The  pressure  of  explosion  will  be 

o  f-OO 

Px  =  JQ^X140  =  480  Ibs.  absolute  ........     (5) 

The  efficiency  of  the  cycle  will  be 

530 

=  48  per  cent  ..........     (6) 


The  quantity  of  heat  added  at  explosion  will  be 

Ha  =  0.169(3500  -1020)=  419  B.T.U  .......     (7) 

The  work  done  per  pound  of  air  will  be 

419X0.480X777.5  =  156,200  ft.-lbs  ........      (S) 

The  pressure  at  release  will  be 

Pt  =      '    „          =42.9  Ibs.  per  square  inch  ......    '  •     (9) 

The  work  done  per  pound  of  air  may  be  checked  in  the  following  manner.     The 
work  of  compression  is 


The  work  of  expansion  is 

/  ^  ">no\ 

53.3  X  (3500 -530^) 

0307~  =  220,200  ft.-lhs (11) 

The  difference  is  the  net  work  of  the  cycle,  or 

220,200-64,200  =  156,000 ,     .     (12) 

The  net  work  per  cubic  foot  of  swept  volume  per  cycle  is 


'-— - •=  14,650  ft. -Ibs.  per  cubic  foot (13) 

The  mean  effective  pressure  shown  by  the  card  is 

AM|°_=io2  Ibs.  per  square  inch (14) 

The   horse-power  theoretically  developed   by  an   engine   operating   on   this  cycle 
would  be 

14,650  N(Va-Vc) 
33,000 

in  which  N  is  the  number  of  cycles,  or  one-half  the  number  of  revolutions  per  minute. 

The  card  for  the  engine  may  now  be  constructed  by  locating  points  PaVa,  PCVC, 
PXVC,  and  PtVa,  drawing  perpendiculars  between  the  first  and  fourth  and  the  second 


292  THE  INTERNAL  COMBUSTION  ENGINE  ART.  285 

and  third,  and  adiabatics  between  the  first  and  second  and  third  and  fourth.     This  is 
the  card  illustrated  in  Fig.  152. 

285.  Methods  of  Governing  the  Otto  Cycle  Engine.  Four  methods 
are  employed  for  controlling  the  speed  and  amount  of  power  developed, 
in  an  Otto  cycle  engine.  The  first  method  is  to  cause  the  engine  to  miss 
explosions,  thus  reducing  the  number  of  working  strokes  which  the  engine 
makes  in  a  given  time.  This  is  known  as  hit-and-miss  governing.  The 
second  method  is  to  throttle  the  port  through  which  the  charge  enters 
the  engine,  reducing  the  weight  of  charge  taken  in  and  the  power  developed 
by  its  explosion.  This  is  known  as  throttle  governing.  The  third  method 
is  to  reduce  the  proportion  of  combustible  gas  contained  in  the  charge, 
and  so  to  weaken  the  explosion.  The  fourth  method  is  to  delay  the 
instant  of  ignition,  and  so  to  reduce  the  power  developed  by  a  given  weight 
of  charge. 

If  the  power  developed  within  the  cylinder  of  an  Otto  cycle  engine 
equipped  with  a  hit-and-miss  governor  is  greater  than  is  necessary  to  keep 
the  engine  up  to  speed,  the  engine  will  gain  speed.  In  order  to  prevent 
this,  it  is  customary  to  so  arrange  the  governing  mechanism  that  it  will 
prevent  explosions  so  long  as  the  engine  is  operating  at  more  than  normal 
speed.  This  may  be  accomplished  in  several  ways.  One  method  is  to 
cause  the  governor  to  hold  the  exhaust  valve  open  until  the  speed  becomes 
normal.  If  the  inlet  valve  operates  automatically  (i.e.,  if  it  is  opened  by 
the  suction  of  the  piston  and  not  by  some  mechanical  device),  this  will 
prevent  the  engine  from  sucking  in  a  charge  during  the  suction  stroke, 
since  it  will  cause  it  to  take  suction  from  the  exhaust  pipe,  and  no  explosion 
will  occur  at  the  beginning  of  the  next  working  stroke.  A  second  method 
is  to  cause  the  governor  mechanism  to  hold  the  inlet  valve  closed.  A 
third  method  (which  is,  however,  very  seldom  used)  is  to  cause  the  governor 
mechanism  to  hold  the  inlet  valve  open  during  the  compression  stroke. 
When  an  engine  is  equipped  with  heavy  fly-wheels  and  a  sensitive  governor, 
the  hit-and-miss  system  gives  fairly  close  regulation  and  very  great 
economy.  When  extremely  close  speed  regulation  and  uniform  turning 
moment  is  unnecessary,  it  is  the  preferable  method  of  speed  regulation. 

Throttling  the  mixture  as  it  enters  the  engine  cylinder  gives  a  card 
of  the  form  shown  in  Fig.  154.  Line  a  b  is  the  exhaust  stroke,  line  b  d 
is  the  suction  stroke,  line  d  c  the  compression  stroke  and  line  x  t  the  work- 
ing stroke.  The  dotted  lines  show  the  form  of  card  which  would  be  given 
were  there  no  throttling.  The  area  d  e  b  is  the  work  required  to  suck 
the  charge  through  the  throttle,  and  is  a  loss.  Since  the  compression 
pressure  is  reduced,  the  efficiency  of  the  cycle  is  reduced  somewhat,  although 
this  is  partly  counterbalanced  by  the  lower  terminal  pressure  resulting 
from  the  more  complete  expansion  of  the  charge.  This  method  of  gov- 
erning, therefore,  reduces  the  efficiency  of  the  engine.  It  is  mechanically 


ART.  285     METHODS  OF  GOVERNING  THE  OTTO  CYCLE  ENGINE       293 

satisfactory  so  long  as  the  compression  does  not  fall  too  low.  When  it 
does  fall  too  low,  on  account  of  extreme  throttling,  ignition  fails  to  take 
place,  and  other  methods  of  regulation  must  be  resorted  to. 

Throttling  the  inflammable  component  of  the  charge  reduces  the  heat 
added  at  the  instant  of  explosion,  and  therefore  gives  a  card  of  the  form 
shown  in  Fig.  155.  The  card  shown  in  dotted  lines  represents  the  form 


FIG.  154. — Card  given  by  a  throttle 
governed  gas  engine. 


FIG.  155.— Card  given  when  the  gas  is 
throttled. 


of  card  given  with  the  gas  unthrottled.  Theoretically  this  method  of 
governing  makes  no  reduction  in  the  efficiency  of  the  cycle.  Practically 
its  efficiency  is  less  than  that  of  the  hit-and-miss  method.  As  the  mixture 
grows  weaker  it  becomes  more  difficult  to  ignite,  so  that  at  low  loads 
ignition  fails. 

A  fourth  method  of  governing  a  gas  engine  is  to  "  delay  the  spark." 
This  method  is  wasteful,  since  by  retarding  the  ignition  to  some  point 
in  the  working  stroke,  a  portion  of 
the  power  available  is  not  utilized. 
The  form  of  card  produced  may  be 
seen  in  Fig.  156.  The  card  shown 
in  dotted  lines  is  the  one  which  would 
be  given  by  the  same  charge  were 
the  spark  properly  advanced.  It  will 
be  seen  that  a  considerable  amount 
of  power  is  wasted.  This  method  of 
governing  is  used  in  connection  with 
throttle  governing  in  operating  auto- 
mobile or  other  portable  engines 

in  which  it  is  desired  to  vary  the  speed  of  the  engine  as  well  as  the  power. 
This  method  is  there  employed  on  account  of  its  extreme  convenience 
and  adaptability,  in  spite  of  its  inherent  wastefulness. 


\ 


FIG.  156. — Result  of  delayed  ignition. 


294 


THE  INTERNAL  COMBUSTION  ENGINE 


ART.  286 


Combinations  of  any  of  these  methods  of  gas-engine  governing  may  be 
used  in  the  case  of  the  Otto  cycle  engine.  The  usual  method  is  to  use  hit- 
and-miss  governing  alone  where  a  fairly  constant  speed  is  required  in 
stationary  work,  to  use  hit-and-miss  in  connection  with  throttle  governing 
where  a  constant  speed  and  close  regulation  are  required;  and  to  use 
throttle  governing  in  connection  with  delayed  ignition  where  variable 
speed  and  power  are  required  of  the  engine. 

286.  The  Two-cycle  Engine.  The  thermodynamic  principle  of  the 
two-cycle  engine  is  exactly  the  same  as  that  of  the  Otto  cycle  engine. 
The  details  of  the  engine  are,  however,  quite  different.  In  Fig.  157  is 

shown  a  section  of  a  two-cycle  engine.  The 
cylinder  is  an  iron  casting  which  is  water 
jacketed  in  the  manner  shown.  The  crank 
case  b  is  so  arranged  that  it  is  practically  gas 
tight.  During  the  upward  stroke  of  the  piston 
P,  a  charge  is  drawn  into  the  crank  case 
through  the  check  valve  V.  This  charge 
consists  of  a  mixture  of  air  and  combustible 
gas  or  vapor.  When  the  piston  descends,  this 
charge  is  compressed  within  the  crank  case,  its 
pressure  rising  to  from  7  to  12  pounds  gage, 
depending  upon  the  volume  of  the  crank  case. 
When  it  reaches  the  bottom  of  its  stroke,  the 
piston  uncovers  two  ports,  one  on  each  side  of 
the  cylinder.  The  port  at  the  left  marked  E 
is  the  exhaust  port,  while  that  at  the  right 
marked  /  is  the  inlet  port.  Since  the  inlet 
port  connects  the  crank  case  with  the  cylinder, 
the  charge  in  the  crank  case  will  be  forced  into 
the  cylinder  on  account  of  the  difference  in 
pressure.  The  form  of  the  top  of  the  piston 
is  such  that  this  charge  is  directed  upward  and 
into  the  cylinder,  and  as  it  enters,  it  expels  the  gases  contained  within 
the  cylinder  through  the  exhaust  port.  During  the  upward  stroke  of 
the  piston,  the  charge  now  contained  within  the  cylinder  is  adiabatically 
compressed.  When  the  piston  reaches  the  top  of  its  stroke,  the  charge 
is  ignited  by  the  spark  plug  marked  S  and  explodes.  The  piston 
descends  during  the  working  strokeof  the  engine.  During  its  upward 
or  compression  stroke  it  has  sucked  a  fresh  charge  into  the  crank  case 
and  during  its  downward  or  working  stroke  it  compresses  this  charge. 
As  the  piston  reaches  the  end  of  its  stroke,  the  exhaust  port  is  un- 
covered and  the  burned  charge  escapes  from  the  cylinder  on  account 
of  its  pressure.  An  instant  later  the  inlet  port  (which  is  nearer  the 


FIG.   157. — Section  of  a  two- 
cycle  engine. 


ART.  28G 


THE  TWO-CYCLE  ENGINE 


295 


bottom  of  the  cylinder  than  the  exhaust  port)  is  uncovered,  and  the 
crank  case  compression  forces  the  fresh  charge  into  the  cylinder.  It  will 
thus  be  seen  that  the  engine  makes  one  compression  stroke  and  one  work- 
ing stroke  each  revolution. 

It  is  usual  in  small  two-cycle  motors  to  employ  the  crank  case  as  a  pump 
in  the  manner  already  described.  In  large  two-cycle  engines,  separate 
pumps  are  provided  for  compressing  the  gas  and  the  air,  and  the  engine 
is  sometimes  made  double-acting  in  the  manner  shown  in  Fig.  158.  In 
this  engine  the  pumps  deliver  the  charge  to  the  working  cylinder  through 
the  valve  7,  while  the  working  piston  P  is  in  the  position  shown.  The 
entering  charge  expels  the  spent  charge  through  the  ports  marked  P. 
As  the  working  piston  moves  to  the  right  it  compresses  the  fresh  charge, 
which  is  exploded  when  the  piston  reaches  the  end  of  its  stroke.  When 
it  moves  to  the  left,  the  right-hand  charge  is  performing  its  working 


Gas 


-Section  through  the  working  cylinder  of  a  Koerting  two-cycle  double  acting 

engine. 


stroke  while  the  left  hand  charge  is  being  compressed.  The  length  of 
the  piston  is  such  that  the  single  set  of  exhaust  ports  serves  for  both  ends 
of  the  cylinder. 

The  advantages  of  the  two-cycle  over  the  four-cycle  engine  are  that 
it  requires  a  less  number  of  valves  and  that  it  makes  twice  as  many  work- 
ing strokes  in  a  given  number  of  revolutions.  At  low  speed,  a  two-cycle 
engine  gives  nearly  twice  the  power  of  a  four-cycle  engine  of  the  same 
speed  and  size.  At  high  speeds,  however,  a  part  of  the  fresh  charge  is 
apt  to  escape  from  the  cylinder  and  a  part  of  the  spent  charge  is  apt  to 
remain.  This  results  in  a  serious  reduction  in  the  power  and  efficiency  of 
the  two-cycle  engine.  The  theoretical  efficiency  of  the  two-stroke  cycle 
is,  however,  exactly  the  same  as  that  of  the  four-stroke  cycle  having  the 
same  compression  pressure,  and  the  pressures,  temperatures,  volumes,  and 
work  done  are  computed  in  exactly  the  same  manner. 


296 


THE  INTERNAL  COMBUSTION  ENGINE 


ART.  287 


287.  The  Sargent  Cycle  Engine.  The  Sargent  cycle  has  been  developed 
in  order  to  provide  a  cycle  having  a  greater  efficiency  than  the  Otto  cycle, 
and  also  to  provide  better  means  of  speed  regulation  for  engines  of  large 
power.  The  theoretical  card  of  a  Sargent  cycle  engine  is  illustrated  in 
Fig.  159.  In  the  Sargent  cycle,  the  admission  of  the  charge  is  stopped 
at  some  point  during  the  suction  stroke.  This  point  is  marked  A  on  the 
card.  During  the  remainder  of  the  stroke  the  charge  is  expanded  below 
atmospheric  pressure,  its  final  pressure  and  volume  being  represented  by 
the  point  n.  During  compression  stroke  the  charge  is  compressed  to 
the  point  C.  Explosion  then  occurs,  the  pressure  rising  to  point  X. 
Adiabatic  expansion  then  follows,  the  charge  expanding  to  point  L. 
The  exhaust  valve  then  opens  and  the  pressure  falls  to  that  of  the  atmos- 


FIG.  159. — Theoretical  card  from  a  Sargent  cycle  engine. 

phere,  represented  by  point  m.  The  spent  charge  is  now  expelled  from  the 
cylinder.  A  fresh  charge  is  then  drawn  in  during  the  early  part  of  the 
suction  stroke  and  the  cycle  is  repeated.  The  amount  of  power  developed 
is  adjusted  by  causing  the  governor  to  close  the  inlet  valve  at  the  proper 
point  in  the  suction  stroke,  the  valve  closing  early  when  the  power  required 
is  small,  and  remaining  open  until  the  end  of  the  stroke  when  the  max- 
imum power  is  required  of  the  engine. 

It  will  be  seen  from  an  inspection  of  the  Sargent  cycle  card  that  it 
consists  of  two  parts,  a  c  x  t  being  the  equivalent  of  an  Otto  cycle,  and 
a-t-l-m  being  an  additional  amount  of  work  realized  from  the  same 
quantity  of  heat.  The  Sargent  cycle  is  therefore  somewhat  more  efficient 


ART.  287  THE  SARGENT  CYCLE  ENGINE  297 

than  is  the  Otto  cycle,  since  it  expands  the  gas  more  completely,  reducing 
its  terminal  temperature  (i.e.,  the  temperature  at  point  /)  and  therefore 
the  amount  of  heat  rejected. 

The  computations  of  the  pressures,  volumes,  etc.,  of  the  Sargent 
cycle  will  be  as  follows,:  Let  Pa,  V  a,  and  T  a  be  respectively  the  pressure  in 
pounds  per  square  foot,  the  volume  in  cubic  feet,  and  the  absolute  tem- 
perature of  the  charge  at  point  a,  and  designate  the  same  quantities  for 
the  charge  at  points  c,  t,  x,  I,  m,  and  n  by  appropriate  subscripts.  Let 
Ha=the  heat  added  at  explosion  and  Hr  the  heat  rejected  at  exhaust. 
We  will  then  have  for  the  swept  volume  of  the  cycle  Vm  —  Vc.  The  weight 
of  the  charge  will  be 


RTa' 

The  volume  of  the  compression  space  will  be 

i 


(1) 


V   —  V  I 

*  c  ~     y  a\    r> 
v^c 


The  temperature  of  compression  will  be 

•/-- 1 

rji     rj~i    (         '    \  n^    11  /Q\ 

•*•  c  ~~    *  a  \   T)     I  ~   •*•  a  \  ~-ir~~  j (y) 

\*-a  /  \"  c  / 

The  rise  in  temperature  resulting  from  the  explosion  will  be 


The  heat  added  as  a  result  of  the  explosion  will  be 

Ha=WCv(Tx-Tc) 
The  terminal  temperature  will  be 


(6) 

x  l 


1"1-  T  (P'\"r 

v)        Tl\¥x) 

The  fall  in  temperature  at  the  end  of  expansion  will  be 


The  heat  rejected  will  be 

Hr=WCv(Ti-Ta).  (8) 


298  THE  INTERNAL  COMBUSTION  ENGINE  ART.  288 

The  efficiency  of  the  cycle  will  be 

£  =  J¥^ .-•     (9) 

or 


C\(TX-TC) 
or 

v,       Tx-Tc-Ti  +  Ta 


It  will  appear  from  this  equation  that  the  efficiency  of  the  Sargent  cycle, 
unlike  that  of  the  Otto  cycle,  depends  on  the  temperature  of  explosion. 
The  work  represented  by  the  area,  c'  c,  a  a',  is 

P   V  —  P    V  IT  —T 

TJ  •Lc'c-tava          T)  I      c          a 

U~    ~ 


the  work  of  expansion  is 

PxVx-PiVi 


the  work  represented  by  the  area  a'  a.    mm'  is  of  course, 

Uam  =   Pa   (Vm-Va);     .......        (14) 

the  total  work  of  the  cycle  is 

Px  Vx  -Pi  Vl  -  Pc  Vc  +Pa  Va  -Pa  Vm+Pa  Vc 


g)  +2Pa  Va 


288.  The  Diesel  Cycle  Engine.  Another  cycle  which  had  been  em- 
ployed for  the  internal  combustion  engine,  and  which  is  especially  adapted 
for  oil  fuel,  is  known  as  the  Diesel  cycle.  This  also  is  a  four-stroke  cycle, 
and  the  card  is  shown  in  Fig.  160.  During  the  first  or  exhaust  stroke,  the 
products  of  combustion  are  expelled  from  the  cylinder.  During  the 
second  or  suction  stroke,  a  charge  of  pure  air  is  drawn  into  the  cylinder. 
During  the  third  or  compression  stroke,  this  air  is  compressed  from  point 
a  to  point  c,  the  pressure  rising  to  from  500  to  700  pounds  per  square  inch. 


ART.  289 


THE  DIESEL  CYCLE  ENGINE 


299 


At  the  end  of  the  compression  stroke,  as  the  piston  again  moves  forward, 
expanding  the  charge,  a  quantity  of  fuel  is  injected  into  the  cylinder  by 
means  of  a  pump.  As  a  result  of  the  adiabatic  compression,  the  tem- 
perature of  the  air  has  been  raised  to  such  a  value  that  the  fuel  is  kindled 
and  burns  as  it  flows  into  the  cylinder,  imparting  heat  to  the  charge. 
It  was  originally  proposed  that  this  fuel  should  be  injected  at  such  a  rate 
that  the  expansion  of  the  charge  would  be  isothermal,  the  heat  supplied 
by  the  burning  fuel  being  just  equal  to  the  work  performed  by  the  expand- 
ing  charge.  After  the  injection  of  the  fuel  ceases,  the  charge  expands 
adiabatically.  The  isothermal  expansion  line  is  the  line  c  d',  and  the 


c     d 


FIG.  160. — Theoretical  cards  from  a  Diesel  cycb  engine. 

adiabatic  expansion  line,  the  line  d'  er  in  Fig.  160.  Governing  is  effected 
by  increasing  or  decreasing  the  quantity  of  fuel  injected,  which  involves 
a  change  in  the  length  of  the  isothermal,  and  in  the  final  state  of  the  work- 
ing fluid  at  point  e' '.  Increasing  the  quantity  of  fuel  injected  raises  the 
final  temperature  of  the  charge  and  so  reduces  the  efficiency  of  the  cycle. 

Isothermal  expansion  of  the  charge  during  the  fuel  injection  period 
results  in  a  cycle  of  high  thermodynamic  efficiency  for  a  given  tempera- 
ture range.  On  the  other  hand,  it  is  impossible  to  design  a  mechanism 
which  will  inject  the  fuel  at  exactly  the  proper  rate  to  give  isothermal 
expansion,  and  the  mechanical  efficiency  of  the  engine  employing  it  will  be 
small.  It  has  been  shown  in  practice  that  it  is  better  to  admit  the  fuel  at 
such  a  rate  as  to  maintain  the  pressure  practically  constant  during  the 
early  part  of  the  working  stroke.  After  all  the  fuel  has  been  injected, 
adiabatic  expansion  commences. 

The  form  of  card  given  by  such  an  engine  is  shown  in  the  same  figure. 
Line  c  d,  representing  the  isobaric,  and  line  d  e  the  adiabatic  portion  of  the 


300 


THE  INTERNAL  COMBUSTION  ENGINE 


PROBS.  1-4 


expansion  period.  Comparing  this  card  with  the  first  one,  it  will  be  seen 
that  the  ratio  of  the  mean  to  the  maximum  pressure  is  much  greater  in 
the  case  of  isobaric  than  in  the  case  of  isothermal  expansion,  and  that  the 
mechanical  efficiency  of  the  engine  is  correspondingly  better.  In  addi- 
tion, the  engine  employing  isobaric  expansion  gives  much  more  power, 
although  the  parts  of  the  two  engines  must  be  of  the  same  weight  and 
cost.  The  practical  advantages  will  thus  be  seen  to  lie  entirely  with  the 
cycle  which  employs  isobaric  expansion. 

The  methods  of  computing  the  states  of  the  working  fluid  at  the  various 
points  in  the  cycle  are  identical  with  those  employed  for  the  Otto  cycle. 
The  quantities  of  heat  added  or  rejected,  and  the  work  performed  during 
the  several  periods  of  the  cycle  may  be  readily  computed.  With  a  com- 
pression pressure  of  600  pounds  per  square  inch  absolute,  an  original 


1         23456789        10 
Ratio  of  fuel  Injection  Period  to  Working  Stroke. 

FIG.  161. — Relation  between  efficiency  and  fuel  injection  period  for  a  Diesel  cycle 
engine  employing  isobaric  expansion. 

pressure  of  14.7  pounds  per  square  inch,  an  original  volume  of  1  cubic  foot, 
and  an  original  temperature  of  oSO0'  absolute,  the  compression  volume 
will  be  0.0714  cubic  feet,  and  the  compression  temperature  1550°  absolute, 
or  1090°  F.  The  efficiency  of  the  cycle  under  varying  conditions  of  load 
may  be  seen  by  reference  to  Fig.  161,  in  which  the  abscissae  are  swept 
volumes  up  to  the  point  dj  expressed  as  a  per  cent  of  the  total  swept  volume 

100(F6-FC)\  ,.  «  -      - 

^  )  and  ordmates  are  efficiencies. 

a        V  c)      / 


i.e.,  values  of 


(V 


•PROBLEMS 


1.  An  Otto  gas  engine    has  a  compression  pressure    of  90  Ibs.  gage.     Find  the 
temperature  of  compression,  assuming  the  air  temperature  to  be  70°  F. 

Ans.     935°  abs. 

2.  Find  the  efficiency  of  the  cycle.  Ans.     43.3%. 

3.  Find  the  explosion  pressure,  assuming  the  rise  in  temperature  to  be  2500°. 

Ans.     386  Ibs.-abs. 

4.  Find  the  terminal  temperature.  Ans.     1950°  abs. 


PROBS.  5-24  PROBLEMS  301 

5.  Find  the  work  done  per  pound  of  working  fluid.  Ans.     142,300  ft.-lbs. 

6.  Find  the  volume  of  the  compression  space  per  pound  of  working  fluid. 

Ans.     3.31  cu.ft. 

7.  Find  the  terminal  volume  per  pound  of  working  fluid.  Ans.     13.34  cu.ft. 

8.  Find  the  swept  volume  per  pound  of  working  fluid.  Ans.     10.03  cu.ft. 

9.  Find  the  work  done  per  cubic  foot  of  swept  volume  per  cycle  per  pound  of 
working  fluid.  Ans.     14,200  ft.-lbs. 

10.  Assuming  that  a  Sargent  cycle  engine,  having  the  same  compression  as  the 
Otto  cycle  engine  in  Problem  1  and  the  same  explosion  pressure  as  in  Problem  3, 
expands  its  charge  to  atmospheric  pressure,  what  is  the  terminal  volume  per  pound 
of  working  fluid  ?  Ans.     33.6  cu.ft. 

11.  Find  the  work  of  expansion.  Ans.     273,000  ft.-lbs. 

12.  Find  the  work  of  compression.  Ans.     52,700  ft.-lbs. 

13.  Find  the  work  represented  by  the  area  a'  a  mm'  in  Fig.  159. 

Ans.     43,000  ft.-lbs. 

14.  Find  the  net  work  of  the  cycle  per  pound  of  working  fluid. 

Ans.     177,200  ft.-lbs. 
16.  Find  the  heat  added  per  pound  of  working  fluid.  Ans.     423  B.T.U. 

16.  Find  the  efficiency  of  the  cycle.  Ans.     54.0% 

17.  In  a  Diesel  cycle  the  compression  is  carried  to  700  Ibs.  absolute.     The  initial 
temperature  is  70°  F.     Find  the  compression  temperature.  Ans.     1620°  abs. 

18.  Find  the  volume  of  compression  space  per  pound  of  working  fluid. 

Ans.     0.86  cu.ft. 

19.  Assuming  that  the  temperature  of  the  working  fluid  is  doubled  during  isobaric 
expansion,    find    the    work    done     per    pound    of    working    fluid     during    isobaric 
expansion.  Ans.     86,600  ft.-lbs. 

20.  Find  the  work  done  per  pound  of  working  fluid  during  compression. 

Ans.     142,000  ft.-lbs. 

21.  Find  the  work  done  per  pound  of  working  fluid  during  adiabatic  expansion. 

Ans.     239,000  ft.-lbs. 

22.  Find  the  net  work  of  the  cycle  per  pound  of  working  fluid. 

Ans.     186,000  ft.-lbs. 

23.  Find  the  heat  added.  Ans.     384  B.T.U. 

24.  Find  the  efficiency  of  the  cycte.  Ans.     61.5%. 


CHAPTER  XX 

NOTES   ON   THE   DESIGN   AND   PERFORMANCE   OF   INTERNAL 
COMBUSTION  ENGINES 

289.  Thermal  Behavior  of  the  Charge  during  Induction  and  Com- 
pression.   In  the  theory  of  the  Otto  cycle  developed  in  the  previous  chapter 
the  charge  entering  the  cylinder  was  assumed  to  have  the  properties 
and  temperature  of  atmospheric  air.     Actually  the  charge  consists  of  a 
mixture  of  air  and  combustible  gas,  and  its  properties  are  therefore  some- 
what different  from  those  of  pure  air.     Since  the  wall  of  the  cylinder  has 
a  temperature  somewhat  higher  than  that  of  the  atmosphere,  the  charge 
is  heated  as  it  enters  the  cylinder.     As  it  is  drawn  into  the  cylinder,  it 
mixes  with  a  considerable  volume  of  spent  charge  whose  temperature  is 
relatively  high.     In  consequence,  the  temperature  of  the  working  fluid 
contained  in  the  cylinder  at  the  beginning  of  compression  is  almost  always 
considerably  higher  than  that  of  the  atmosphere,  and  the  effect  is,  of 
course,  to  reduce  the  power  of  the  engine  by  reducing  the  weight  of  the 
working  fluid. 

During  the  compression  stroke  the  temperature  of  the  charge  rises. 
As  soon  as  its  temperature  exceeds  that  of  the  cylinder  wall,  it  parts  with 
heat  by  conduction  and  radiation.  The  compression  is  therefore  not 
adiabatic,  but  is  approximately  poly  tropic,  the  actual  compression  line 
lying  between  the  adiabatic  and  the  isothermal  lines.  The  index  of  the 
compression  line  ranges  from  1.25  to  1.35,  its  exact  value  depending  upon 
the  size,  the  speed,  and  the  design  of  the  engine.  In  general  the  index 
of  the  compression  curve  will  have  a  high  value  in  the  case  of  a  large 
fast-running  engine  with  a  small  area  of  wall  surface  exposed  to  the  charge, 
and  will  have  a  low  value  when  the  opposite  conditions  obtain.  Leakage 
has  the  same  apparent  effect  upon  the  form  of  the  compression  curve  as 
does  heat  absorption  by  the  cylinder  wall,  and,  like  it,  produces  more 
serious  effects  in  small  or  slow-speed  than  in  large  or  high-speed  engines. 
Leakage,  however,  is  more  detrimental  than  heat  absorption  in  its  effects 
upon  the*power  and  efficiency  of  the  engine. 

290.  Thermal  Behavior  of  the  Charge  during  Ignition  and  Expansion. 
At  the  end  of  the  compression  stroke,  combustion  begins.     In  develop- 
ing the  theory  of  the  Otto  cycle,  it  was  assumed  that  combustion  took 
place  instantly.     Such  is  not  the  case  in  practice,  since  combustion  is  a 

302 


ART.  290 


THERMAL  BEHAVIOR  OF  THE  CHARGE 


303 


chemical  reaction,  and  a  chemical  reaction  is  a  progressive  and  not  an 
instantaneous  process.  The  rate  at  which  a  reaction  occurs  is  variable, 
depending  upon  the  temperature  and  density  of  the  reacting  substances, 
and  upon  the  extent  to  which  they  are  diluted  by  inert  substances  and  the 
compounds  produced  by  the  reaction.  The  result  of  the  combustion  is  to 
greatly  increase  the  temperature  of  the  charge,  to  reduce  the  density 
of  the  reacting  substances,  and  to  dilute  them  with  the  products  of  com- 
bustion. Each  of  these  effects  reduces  the  rate  at  which  the  reaction 
progresses,  so  that  although  it  is  rapid  at  first,  the  rate  quickly  drops  off, 
and  the  reaction  in  theory  takes  an  infinite  time  for  its  completion. 
When  the  temperature  of  the  exploding  charge  reaches  a  value  of  about 
3300°  to  3600°  absolute,  which  it  does  almost  immediately,  the  reaction 


Suction  Line  -* 


FIG.  162. — Actual  and  theoretical  Otto  cycle  cards  compared. 

practically  ceases,  and  further  combustion  takes  place  only  after  the 
temperature  begins  to  fall.  This  phenomenon  is  known  as  delayed  com- 
bustion, as  suppressed  combustion,  and  as  dissociation. 

As  a  result  of  the  comparatively  gradual  and  incomplete  combustion 
of  the  charge,  the  rise  in  pressure  resulting  from  the  explosion  takes  an 
appreciable  time,  which  modifies  the  card  by  giving  it  the  form  shown  in 
Fig.  162,  where  the  explosion  line  c-x  is  curved  instead  of  being  vertical, 
as  would  be  the  case  were  the  combustion  instantaneous.  Further- 
more the  temperature  and  pressure  realized  as  a  result  of  the  explosion 
are  only  a  fraction  of. what  they  would  be  were  the  combustion  instant 
and  complete.  Hence  in  order  to  obtain  a  given  rise  in  pressure,  and 
therefore  a  given  quantity  of  work  from  the  charge,  it  is  necessary  to  use 
a  larger  quantity  of  fuel  than  theory  would  indicate.  The  actual  efficiency 


304  NOTES  ON  INTERNAL  COMBUSTION  ENGINES  ART.  291 

of  the  engine  is  therefore  seriously  reduced  by  the  phenomenon  of  sup- 
pressed combustion.  The  most  of  the  fuel  remaining  unburned  at  point 
x  begins  to  burn  as  soon  as  the  adiabatic  expansion  of  the  charge  permits 
of  a  sufficient  fall  in  temperature.  This  is  known  as  after  burning.  The 
combustion  is  not  absolutely  complete  at  the  end  of  the  expansion  stroke, 
but  it  is  usually  so  far  completed  that  only  slight  traces  of  unburned  gases 
can  be  discovered  in  the  exhaust. 

The  temperature  of  the  charge,  as  a  result  of  the  explosion,  usually 
reaches  a  value  of  from  3000°  to  3600°  absolute.  At  these  extreme  tem- 
peratures gases  readily  part  with  heat  to  their  surroundings  by  conduc- 
tion and  radiation.  The  walls  of  the  cylinder  are  of  course  cooled  by  a 
water  jacket  or  other  suitable  means.  Since  the  jacket  maintains  the 
walls  at  a  temperature  usually  ranging  from  150°  to  250°,  the  rate  at  which 
the  gases  give  up  heat  to  the  walls  is  very  great.  That  portion  of  the 
charge  which  is  in  immediate  contact  with  the  wall  is  cooled  by  con- 
duction almost  to  the  temperature  of  the  wall  itself.  The  remainder 
of  the  charge  is  at  a  very  much  higher  temperature  and  radiates  its  heat 
to  the  wall.  As  a  result  of  the  phenomenon  of  after  burning  the  charge 
receives  heat  during  the  working  stroke.  At  the  same  time,  it  is  losing 
heat  by  conduction  and  radiation  to  the  cylinder  walls  and  by  transform- 
ing it  into  the  work  of  expansion.  The  expansion  which  takes  place 
during  the  working  stroke  is  therefore  not  adiabatic,  and  the  rate  of  heat 
transfer  is  usually  such  that  more  heat  is  lost  to  the  wall  than  is  gained 
from  the  after  burning  of  the  charge.  The  index  of  the  expansion  line 
is  therefore  usually  somewhat  greater  than  the  index  of  the  adiabatic 
expansion  line,  sometimes  ranging  as  high  as  1.7,  although  its  usual  value 
lies  between  1.41  and  1.45.  The  same  operating  conditions  which  tend 
to  reduce  the  heat  loss  to  the  cylinder  wall  during  the  compression  stroke 
tend  to  reduce  the  heat  loss  during  the  working  stroke,  but  whereas  these 
conditions  tend  to  raise  the  value  of  the  index  of  the  compression  curve, 
they  tend  to  lower  the  value  of  the  index  of  the  expansion  curve. 

291.  Form  of  the  Actual  Card.  The  form  of  the  actual  card  obtained 
from  an  Otto  cycle  engine  is  that  shown  in  full  lines  in  Fig.  162.  The 
line  which  would  be  obtained  were  the  compression  of  the  charge  adiabatic 
is  the  dotted  line  ac'.  It  will  be  noted  that  the  actual  compression  pres- 
sure is  less  than  that  which  would  result  from  adiabatic  compression. 
In  consequence,  the  actual  compression  temperature  will  also  be  con- 
siderably less  than  that  resulting  from  adiabatic  compression,  and  the 
efficiency  of  the  actual  cycle  will  therefore  be  less  than  the  efficiency 
of  theoretical  cycle. 

Were  the  combustion  of  the  charge  instantaneous,  the  line  ex  would 
be  vertical.  Since  such  is  not  the  case,  the  line  will  have  the  general 
form  shown;  its  exact  form  depending  on  the  instant  at  which  ignition 


ART.  292  LOSSES  IN  THE  GAS  ENGINE  305 

commences,  the  speed  and  size  of  the  engine,  the  character  of  the  charge, 
etc. 

The  actual  expansion  line  x-t,  falls  below  the  adiabatic  expansion  line, 
x't' ',  since  its  index  is  greater  than  the  index  of  the  adiabatic  line.  Were 
the  entire  heat  of  combustion  contained  in  the  ,charge  utilized  in  instantly 
raising  its  temperature,  and  were  the  specific  heat  of  the  charge  constant, 
its  pressure  would  rise  to  the  point  x"  as  a  result  of  the  explosion,  the 
adiabatic  expansion  line  would  be  the  line  x"  t" ,  and  the  work  of  the  cycle 
would  be  very  greatly  increased.' 

On  account  of  wire  drawing  and  fluid  friction,  the  corner  of  the  card 
at  t  is  rounded,  and  the  suction  line  falls  below  the  exhaust  line  in  the 
manner  already  shown  in  Fig.  154.  This  results  in  reducing  the  pressure 
at  the  beginning  of  compression,  and  the  loop  enclosed  between  the  suc- 
tion and  exhaust  lines  represents  negative  work. 

292.  Losses  in  the  Gas  Engine.  The  losses  which  occur  in  an  Otto 
cycle  engine  may  be  classified  as  follows: 

First:  Losses  due  to  delayed  or  suppressed  combustion. 

Second:  Losses  due  to  the  radiation  and  conduction  of  heat  to  the 
cylinder  walls. 

Third :  Losses  due  to  the  leakage  of  the  charge. 

Fourth:  Exhaust  losses  or  losses  due  to  the  sensible  heat  of  the  charge 
at  the  termination  of  expansion. 

Fifth:  Losses  due  to  fluid  friction  and  wire  drawing  of  the  charge. 

Sixth:  Losses  due  to  the  mechanical  friction  of  the  engine. 

It  is  obvious  that  the  efficiency  of  the  actual  cycle  must  always  be 
less  than  that  of  the  theoretical  cycle.  Hence  the  sum  of  the  six  losses  is 
always  greater  than  the  exhaust  loss  of  the  theoretical  Otto  cycle  having 
the  same  compression  pressure,  and  supplied  with  the  same  quantity 
of  heat  energy.  The  theoretical  loss  made  necessary  by  the  form  of  the 
cycle  can  be  reduced  only  by  increasing.the  compression  pressure.  As  the 
compression  pressure  is  increased,  the  explosion  pressure  is  increased  in 
very  nearly  the  same  proportion.  This  makes  necessary  a  corresponding 
increase  in  the  strength  and  weight  in  the  parts  of  the  engine,  and  increases 
the  cost  of  its  construction.  Compression  pressures  higher  than  200 
pounds  gage  are  therefore  not  practicable  except  when  very  lean  fuels 
are  employed.  When  fuels  of  high  heating  value  (such,  for  instance,  as 
gasoline  vapor),  are  employed,  the  compression  pressure  must  be  much 
less  than  200  pounds  in  order  to  avoid  excessive  explosion  pressures. 

The  effect  of  delayed  combustion  is,  of  course,  to  reduce  the  explosion 
pressure  and  therefore  to  reduce  the  amount  of  work  performed  during 
the  cycle  and  the  efficiency  of  the  engine.  Were  the  charge  to  reach  the 
temperature  which  would  result  from  complete  combustion,  the  loss  to 
the  cylinder  walls  would  be  greater  than  is  actually  the  case.  Since  .the 


306  NOTES  ON  INTERNAL  COMBUSTION  ENGINES  ART.  292 

combustion  of  the  charge  continues  during  the  working  stroke,  a  small 
part  of  the  heat  so  developed  is  transformed  into  work,  but  the  most  oJ 
it  is  rejected  in  the  sensible  heat  of  the  exhaust.  Any  portion  of  the  charge 
remaining  unburned  at  the  instant  of  release  is,  of  course,  rejected  and  the 
potential  heat  contained  in  it  is  lost.  The  effect  of  suppressed  combustion 
is  therefore  to  increase  the  loss  in  the  exhaust  and  to  decrease  the  loss 
to  the  water  jacket.  The  loss  from  suppressed  combustion  may  be 
diminished  by  the  employment  of  a  lean  charge  (i.e.,  one  which  has  a 
comparatively  low  heating  value).  The  effect  of  the  lean  charge  is  to 
reduce  the  theoretical  maximum  temperature  of  explosion,  and  therefore 
to  make  possible  a  quicker  and  a  more  complete  burning  of  the  charge. 

The  effect  of  the  heat  transfer  from  the  charge  to  the  walls  of  the 
cylinder,  where  it  is  absorbed  by  the  jacket  water,  is  to  reduce  the  work 
required  for  compression,  the  explosion  pressure,  and  the  work  done  dur- 
ing the  expansion  stroke.  The  net  result  is  that  the  work  done  during 
the  cycle  is  diminished  somewhat,  and  the  efficiency  of  the  cycle  is  unfav- 
orably affected.  A  considerable  part  of  the  heat  transferred  to  the  water 
jacket  is,  however,  heat  that  would  otherwise  be  rejected  at  exhaust, 
and  the  amount  of  heat  lost  to  the  water  jacket  is  not  a  true  measure 
of  the  power  and  efficiency  lost  as  a  result  of  water  jacketing.  While 
it  is  well  to  reduce  the  jacket  loss  to  minimum,  it  is  not  as  serious  in  its 
effects  upon  the  engine  efficiency  as  are  other  forms  of  losses. 

The  effect  of  leakage  during  the  compression  stroke  is  to  allow  a 
portion  of  the  charge  to  escape  after  work  has  been  done  upon  it,  but 
before  it  has  returned  any  portion  of  this  work.  Furthermore  it  carries 
away  the  potential  heat  of  combustion,  which  is,  of  course,  entirely  lost. 
Leakage  during  the  expansion  stroke  does  not  affect  the  efficiency  of  the 
engine  so  seriously,  but  it  does  produce  some  loss  by  lowering  the  mean 
pressure  during  the  expansion  period.  It  might  be  thought  that  on 
account  of  the  high  pressures  employed,  leakage  would  be  a  serious  matter 
in  the  case  of  the  gas  engine.  When,  however,  the  valves,  the  piston, 
the  cylinder,  and  the  rings  are  in  good  order,  no  appreciable  leakage 
can  take  place. 

The  exhaust  loss  may  be  reduced  by  expanding  the  charge  more 
completely,  as  is  done  in  the  Sargent  cycle  engine.  The  additional  amount 
of  work  obtainable  in  this  way  is  not,  however,  very  great,  as  may  be 
seen  by  reference  to  Fig.  159,  in  which  the  area  a  t  I  m  represents  the 
power  usually  obtained  in  such  a  cycle  from  the  exhaust  losses  of  the  Otto 
cycle.  It  will  be  seen  that  the  area  in  question  is  a  rather  small  portion 
of  the  entire  area  of  the  card.  It  has  often  been  proposed  to  save  some 
of  the  exhaust  loss  by  compounding  the  gas  engine  (i.e.,  by  discharging 
the  exhaust  from  the  first  cylinder  into  a  larger  cylinder  in  which  it  may 
be  more  completely  expanded).  It  will  usually  be  found,  however, 


ART.  293  LIMITS  OF  THE  ROTATIONAL  SPEED  307 

that  the  amount  of  work  realized  after  deducting  the  extra  losses  incurred 
in  transferring  the  charge  from  one  cylinder  to  another,  will  not  be 
sufficient  to  overcome  the  friction  of  the  added  cylinder.  The  employ- 
ment of  the  Sargent  cycle  is  a  preferable  alternative  for  utilizing  the 
available  energy  of  the  exhaust. 

The  Tosses  due  to  friction  and  wire  drawing  of  the  charge  may  be 
reduced  by  the  employment  of  large  valves  which  are  opened,  promptly 
by  properly  designed  mechanism.  These  losses  increase  with  the  speed 
of  the  engine,  but  do  not  become  serious  at  the  speeds  ordinarily  employed 
in  stationary  practice. 

The  conditions  of  high  mechanical  efficiency  in  the  gas  engine  are 
the  same  as  in  the  steam  engine.  It  is  not  possible,  however,  to  improve 
the  mechanical  efficiency  of  the  gas  engine  by  compounding,  as  may 
be  done  in  the  case  of  the  steam  engine.  The  mechanical  efficiency  of 
the  gas  engine  may  be  improved  only  by  careful  attention  to  the  details 
of  the  design  of  the  mechanism  and  to  the  lubricating  system.  The 
friction  losses  are  usually  from  50  to  100  per  cent  higher  in  gas  engines 
than  in  steam  engines  of  equal  power. 

It  will  be  seen  from  the  above  discussion  that  the  conditions  which 
favorably  affect  the  efficiency  of  the  gas  engine  are,  in  general,  a  high 
speed  of  rotation,  the  use  of  units  of  large  power,  the  adoption  of  that 
form  of  cylinder  which  reduces  the  wall  area  per  pound  of  charge  per 
cycle  to  a  minimum,  and  the  employment  of  a  lean  charge.  The  most 
serious  loss  is  that  due  to  the  delayed  combustion  of  the  charge.  The 
Diesel  cycle  engine  avoids  the  difficulty  of  delayed  combustion  and  there- 
fore gives  promise  of  higher  practical  efficiency  than  does  the  Otto  cycle 
engine,  although  other  forms  of  loss  (e.g.,  loss  due  to  leakage)  produce 
more  serious  results  in  the  Diesel  engine  than  in  the  Otto  engine. 

293.  Limits  of  the  Rotational  Speed  of  Internal  Combustion  Engines. 
It  has  already  been  pointed  out  that  the  higher  the  speed  at  which  a 
gas  engine  operates,  the  greater  will  be  its  efficiency.  At  ordinary  speeds 
the  power  of  the  engine  is  increased  by  increasing  the  speed,  since  at 
ordinary  speeds  the  work  per  cycle  remains  practically  constant,  and  the 
number  of  cycles  increases  in  direct  proportion  to  the  speed.  It  is  not 
possible,  however,  to  indefinitely  increase  the  power  of  an  internal  com- 
bustion engine  by  increasing  its  speed.  As  the  speed  of  the  engine 
increases,  the  effect  of  wire  drawing  in  reducing  the  quantity  of  charge 
taken  in  per  cycle  also  increases.  At  speeds  below  400  or  500  revolu- 
tions per  minute,  this  effect  is  scarcely  noticeable  when  the  engine  is 
equipped  with  mechanically  operated  valves.  At  speeds  greater  than 
this,  however,  the  net  work  per  cycle  gradually  falls  off  on  account  of 
the  wire  drawing  of  the  charge.  The  speed  at  which  the  power  of  the 
engine  reaches  its  maximum  value  depends  upon  the  size  and  form  of 


308  NOTES  ON  INTERNAL  COMBUSTION  ENGINES         ART.  294 

the  valves  and  ports.  In  general  the  larger  and  straighter  the  gas 
passages,  the  higher  will  be  the  speed  at  which  the  maximum  power 
of  the  engine  is  realized.  With  ports  of  the  usual  proportions,  it  will 
be  found  that  small  two-cycle  engines  deliver  their  maximum  power 
at  from  700  to  900  revolutions  per  minute,  while  four-cycle  engines 
deliver  their  maximum  power  at  from  1200  to  1800  revolutions  per  minute. 
At  speeds  higher  than  this,  the  quantity  of  charge  taken  per  cycle  by 
the  engine  diminishes  at  a  faster  rate  than  the  speed  increases  and  the 
power  of  the  engine  falls  off.  At  very  high  speeds,  ignition  fails  from 
lack  of  sufficient  compression  of  the  charge,  and  the  speed  of  the  engine 
finally  reaches  a  maximum  where  the  power  developed  is  just  equal 
to  that  absorbed  by  friction. 

In  the  case  of  stationary  engines,  the  speed  is,  of  course,  very  much 
lower  than  in  automobile  and  other  light  high-speed  engines.  The  usual 
speed  for  very  large  engines  (i.e.,  engines  of  over  1000  horse-power) 
is  from  75  to  150  revolutions  per  minute,  the  present  tendency  being 
to  increase  these  speeds.  In  the  case  of  single-acting  stationary  engines, 
the  speed  is  usually  from  200  to  300  revolutions  per  minute,  although 
higher  speeds  are  possible.  As  a  usual  thing,  the  speed  of  a  large  gas  engine 
is  limited  by  the  highest  speed  at  which  the  valve  motion  will  work 
quietly  and  without  undue  wear.  It  will  thus  be  seen  that  the  speed  of 
a  gas  engine  is  really  limited  by  the  design  of  its  parts,  and  will  of 
necessity  be  lower  in  the  case  of  a  large  engine  having  heavy  parts  than 
in  the  case  of  a  small  engine  having  light  parts.  There  is  no  reason, 
however,  why  much  higher  speeds  may  not  be  employed  in  stationary 
service,  with  an  accompanying  gain  in  economy  of  operation. 

294.  The  Design  of  Internal  Combustion  Engines.  In  designing  an 
internal  combustion  engine,  it  is  usually  sufficient  to  assume  that  the 
charge  is  taken  in  at  atmospheric  pressure  and  temperature,  that  the 
compression  and  expansion  lines  are  polytropic,  that  the  index  of  the 
compression  line  is  1.35,  that  the  index  of  the  expansion  line  is  1.45,  that 
the  explosion  occurs  instantly,  that  the  rise  in  temperature  as  a  result 
of  the  explosion  is  2500°,  that  the  specific  heats  of  the  charge  are  those 
of  pure  air;  that  the  card  factor  is  about  90  per  cent,  and  that  the 
mechanical  efficiency  of  the  engine  is  85  per  cent.  Where  actual  cards 
from  engines  of  practically  similar  design  and  approximately  the  same 
speed  are  available,  corrections  may  be  made  in  these  figures.  The 
work  of  compression  and  of  expansion  per  pound  of  working  fluid  may 
be  computed  by  the  methods  outlined  in  Art.  283.  Their  difference 
is  the  net  work  per  pound  of  working  fluid.  The  volume  per  pound 
of  working  fluid  at  the  beginning  and  end  of  compression  is  next  com- 
puted. The  difference  between  these  two  volumes  is  the  swept  volume 
per  pound  of  working  fluid.  Dividing  this  into  the  net  work  per  pound 


ART.  295 


METHODS  OF  IGNITION 


309 


of  working  fluid,  we  will  have  the  net  work  per  cubic  foot  of  swept  vol- 
ume per  cycle,  a  quantity  which  we  may  designate  by  the  letter  W. 
The  indicated  horse-power  of  the  engine  will  then  be 


HP 


0.9  T7  7  N 
33.000     ' 


in  which  HP  is  the  indicat&d  horse-power  of  the  engine,  W  is  the  net 
work  per  cubic  foot  of  swept  volume  per  cycle,  N  is  the  number  of  cycles 
(i.e.,  explosions)  per  minute,  and  V  is  the  swept  volume  of  the  cylinder 
in  cubic  feet.  The  brake  horse-power  of  the  engine  at  maximum  load 
will  be  about  85  per  cent  of  its  indicated  horse-power  at  maximum  load. 
A  gas  engine  is  usually  rated  at  from  2/3  to  3/4  of  the  maximum  brake  horse- 
power which  can  be  obtained  under  the  most  favorable  conditions  of 
operation. 

After  obtaining  the  cylinder  dimensions  and  the  form  of  card,  the 
remainder  of  the  design  of  a  gas  engine  is  a  matter  of  proportioning  the 
parts  to  properly  resist  the  strains  which  come  upon  them,  and  to  arrange 
the  valve  mechanism  so  that  it  operates  with  a  minimum  of  shock  and 
wear.  The  design  of  the  details  of  a  gas  engine  is  very  similar  to  the 
design  of  the  same  parts  of  a  steam  engine,  the  only  difference  being 
produced  by  the  greater  shocks  and  higher  pressures  encountered  in 
gas  engine  work,  and  the  necessity  of  thoroughly 
water-jacketing  or  otherwise  cooling  all  parts 
exposed  to  the  working  fluid. 

295.  Methods  of  Ignition.  Three  methods  have 
been  employed  for  igniting  the  charge  of  a  gas  engine, 
namely,  by  an  electric  spark,  by  contact  with  hot 
metal,  or  by  contact  with  a  flame.  The  latter  method, 
although  formerly  much  used,  is  now  completely  out 
of  date,  while  the  second  method,  known  as  hot  tube 
ignition,  is  seldom  used  except  for  stationary  engines 
operating  on  natural  gas.  In  the  early  types  of  gas 
engines  in  which,  little  or  no  compression  was  used,  a 
flame  was  kept  burning  in  a  separate  chamber  and  by 
opening  a  slide  valve  in  a  passage  connecting  this 
chamber  with  the  cylinder  of  the  eng'ne  at  the  proper 
pc  hit  in  the  stroke,  the  flame  was  communicated  to 
the  charge.  So  long  as  the  compression  pressure  was 
low,  and  the  service  required  of  the  engine  was  not 
severe,  this  method  of  ignition  was  fairly  satisfactory. 
It  was,  however,  soon  superseded  by  the  method  known 
as  hot  tube  ignition. 

The  hot  tube  igniter,  which  is  illustrated  in  Fig.  163,  consists  of  a  passage  hi  the 
cylinder  wall  which  terminates  in  a  tube  of  wrought  iron  or  nickel,  kept  heated  by 
means  of  an  argand  flame  which  surrounds  it.  At  the  beginning  of  the  compression 
stroke,  the  tube  is  filled  with  spent  charge.  As  the  compression  proceeds,  the  spent 


FIG.  163. — Hot-tube  igniter. 


310 


NOTES  ON  INTERNAL  COMBUSTION  ENGINES 


ART.  295 


charge  is  compressed  into  the  hot  part  of  the  tube  and  finally,  near  the  end  of  the 
compression  stroke,  some  of  the  fresh  charge  enters  the  hot  part  of  the  tube  and  is 
ignited.  By  its  expansion,  a  flame  is  forced  into  the  cylinder,  and  the  main  body 
of  the  charge  thus  ignited.  It  will  be  seen  that  the  point  in  the  cycle  at  which  the 
explosion  occurs  depends  upon  the  relative  volume  of  the  hot  tube  and  the  connecting 
passage,  and  upon  the  degree  of  compression.  If  ignition  fails,  or  is  too  late,  the 
volume  of  the  hot  tube  must  be  increased.  If  ignition  is  early,  the  length  and  volume 
of  the  connecting  passage  must  be  increased,  or  the  volume  of  the  tube  decreased. 
Other  things  being  equal,  the  higher  the  degree  of  compression,  the  earlier  the  time  of 
ignition.  So  long  as  the  quality  of  the  fuel  supplied  to  the  engine  is  uniform  and  the 
conditions  of  operation  are  steady,  hot  tube  ignition  is  fairly  satisfactory  with  com- 
paratively high  compression  pressures.  It  can  only  be  used,  however,  with  hit-and- 
miss  governing. 

Electric  ignition  is  effected  in  either  of  two  ways,  the  first  being  known  as  the 
"jump  spark"  method  and  the  second  as  the  " make-and-break  spark"  method.  The 
principle  of  the  jump  spark  is  illustrated  in  the  diagram  shown  in  Fig.  164.  In  this 


FIG.  164. — Diagram  of  a  jump  spark  ignition  apparatus. 

diagram  a-a  are  two  platinum  terminals  contained  within  the  cylinder  of  the  engine 
in  contact  with  the  charge  and  separated  by  about  Vs2  of  an  inch.  These  terminals 
are  connected  with  the  induction  coil  shown,  which  gives  a  high  voltage.  At  the 
proper  time  in  the  revolution  of  the  engine,  a  connection  is  made  in  the  primary 
circuit  of  this  coil  by  means  of  a  commutator  or  contact  maker  operated  by  the  engine. 
The  flow  of  primary  current  through  the  coil  produces  a  secondary  current  of 
immensely  higher  voltage  and  much  lower  amperage,  which  passes  between  the 
terminals  of  the  spark  plug,  igniting  the  charge.  B  is  a  battery  or  other  source  of 
current  for  the  primary  circuit  of  the  induction  coil.  This  current  passes  through 
the  commutator  c  when  it  is  in  the  position  shown,  thence  through  the  vibrator  V, 
through  the  primary  circuit  d  and  back  to  the  battery.  The  vibrator  is  a  device  for 
interrupting  the  current  and  causes  the  primary  current  to  be  pulsating  in  character. 
The  secondary  current,  which  is  induced  by  the  presence  of  the  pulasting  primary 
current,  is  similar  in  character,  but  since  the  primary  circuit  of  the  induction  coil 
consists  of  only  a  few  turns,  while  the  secondary  circuit  consists  of  many  hundreds 
of  turns  of  wire,  all  wound  around  a  soft  iron  core,  the  voltage  of  the  secondary  current 
will  be  sufficiently  great  to  force  it  to  jump  the  terminals  of  the  spark  plug.  These 


ART.  296 


CARBURETORS 


311 


terminals  must  of  course  be  carefully  insulated  from  one  another  or  the  current  will 
be  short-circuited  instead  of  passing  through  the  charge  which  is  to  be  inflamed.  A 
condenser  /  is  usually  connected  into  the  primary  circuit  of  the  induction  coil  in  order 
to  increase  the  effectiveness  of  the  apparatus. 

The  apparatus  used  for  the  make -and -break  spark  is  much  simpler,  although  it  has 
the  disadvantage  of  employing  a  movable  part  within  the  cylinder.  The  current 
originates  in  a  battery  B  as  shown  in  Fig.  165,  passes  through  the  spark  coil  C,  which 
is  a  coil  of  wire  surrounding  a  soft  iron  core,  through  the  platinum  terminals  of  the 
make-and-break  spark  plug  P,  and  then  returns  to  the  battery.  At  the  instant  when 
it  is  desired  to  inflame  the  charge,  the  terminals  being  in  contact,  they  are  quickly 
separated  and  an  arc  is  created  which  effects  ignition.  The  purpose  of  the  spark 
coil  C  is  to  intensify  the  arc  by  its  inductive  action.  In  order  to  economize  current 


I       I 


illinium 


FIG.  165. — Diagram  of  a  make-and-break  ignition  apparatus. 

the  mechanism  of  the  spark  plug  is  made  in  such  a  way  that  the  terminals  are  sepa- 
rated until  just  before  the  spark  is  to  be  produced,  when  they  come  together  for  the 
instant  just  preceding  the  breaking  of  the  circuit. 

296.  Carburetors.  For  portable  internal-combustion  engines  such  as 
are  used  in  automobiles,  launches,  etc.,  it  is  customary  to  use  as  the  fuel 
a  hydro-carbon  vapor  usually  obtained  by  the  evaporation  of  gasoline. 
The  gasoline  is  evaporated  and  mixed  with  the  air  which  forms  the 
remainder  of  the  charge,  in  an  apparatus  known  as  a  carburetor.  Gas- 
oline, when  sprayed  into  air,  rapidly  evaporates  at  all  ordinary  temper- 
atures, and  fills  the  air  with  its  vapor.  If  the  air  is  allowed  to  become 
saturated  with  the  gasoline  vapor,  the  quantity  of  vapor  contained  in 
the  air  will  be  so  great  that  the  mixture  is  not  explosive.  A  charge  in 
which  too  little  gasoline  vapor  is  mixed  with  the  air,  will  also  fail  to 
ignite.  The  office  of  the  carburetor  is  then  to  introduce  into  the  current 
of  jiir  entering  the  cylinder  of  the  engine,  a  proper  quantity  of  gasoline, 


312 


NOTES  ON  INTERNAL  COMBUSTION  ENGINES         ART.  296 


in  such  a  manner  that  it  will  be  completely  evaporated  and  thoroughly 
mixed  with  the  air. 

The  simplest  form  of  carburetor  is  illustrated  in  principle  in  Fig. 
166.  It  consists  of  a  bowl  or  reservoir  in  which  the  gasoline  is  main- 
tained at  a  constant  level  by  means  of  a  float  feed-valve.  This  valve 
consists  of  a  ring  r,  usually  of  cork,  attached  to  a  lever  and  pivoted  in 
such  a  way  that  when  the  level  of  the  gasoline  sinks,  the  weight  of  the 
float  will  open  the  feed  valve  /,  admitting  more  gasoline.  From  this 
chamber  the  gasoline  flows  to  a  small  nozzle  n,  through  a  valve  termed 

the  needle  valve.  By  varying 
the  opening  of  this  needle 
valve,  the  quantity  of  gasoline 
delivered  through  it  in  a  given 
time  by  a  given  head  of  gaso- 
line, may  be  varied.  The 
needle  valve  is  placed  in  a 
restricted  passage  in  the  air 
inlet.  During  the  suction  stroke 
of  the  engine,  a  quantity  of 
air  is  drawn  through  this  re- 
stricted passage  at  high  veloc- 
ity, and  in  consequence,  the 
pressure  of  the  air  in  the 
passage  is  less  than  the  pres- 
sure of  the  atmosphere.  The 
difference  in  pressure  causes  a; 
jet  of  gasoline  to  flow  from  the 
needle  valve  in  the  form  of  a 
fine  spray,  and  to  mix  with 
the  on-rushing  current  of  air. 
A  second  supply  of  air  is 
taken  through  the  check 
valve  v,  termed  the  auxiliary 
inlet,  at  a  point  beyond  the 

needle  valve,  and  mixes  with  the  air  containing  the  gasoline  vapor. 
By  adjusting  the  level  of  the  gasoline  in  the  float-feed  chamber, 
the  opening  of  the  needle  valve,  and  the  strength  of  the  spring  con- 
trolling the  opening  of  the  auxiliary  air  inlet,  the  quantity  of  gasoline 
vapor  in  the  charge  of  air  may  be  controlled  and  a  correct  mixture  obtained 
at  all  ordinary  engine  speeds.  Most  forms  of  carburetors  at  present  on 
the  market  are  modifications  of  the  apparatus  described.  The  arrange- 
ment of  the  several  parts  and  the  general  appearance  of  the  apparatus 
varies  greatly.  In  some  forms  of  the  carburetor,  however,  the  air  is 


FIG.  166. — Simplified  diagram  of  a  carburetor. 


ART.  297    THE  TESTING  OF  INTERNAL  COMBUSTION  ENGINES        313 

drawn  over  a  small  quantity  of  gasoline  contained  in  a  bowl,  instead  of 
spraying  the  gasoline  into  the  air.  Such  carburetors  are  not  generally 
provided  with  auxiliary  air  inlets. 

A  float-feed  carburetor  is  not  usually  used  for  furnishing  gasoline  vapor 
to  stationary  engines.  In  the  cas&  of  stationary  engines,  the  speed  is 
usually  constant  and  the  range  of  adjustment  required  of  the  gasoline 
vaporizer  is  very  much  less.  In  some  cases,  the  incoming  change  of 
air  is  draWh  over  a  pan  in  which  the  gasoline  is  maintained  at  constant 
level.  In  other  cases  the  gasoline  is  simply  allowed  to  leak  through  a 
noedle  valve  into  the  pipe  through  which  the  air  supply  is  drawn. 
Neither  method  of  vaporization  is  as  satisfactory,  however,  as  the  use 
of  a  carburetor. 

297.  The  Testing  of  Internal  Combustion  Engines.  The  following 
quantities  must  be  determined  in  making  a  complete  test  of  an  internal 
combustion  engine  of  the  Otto  type. 

First,  the  pressure  and  temperature  of  the  atmosphere  and  of  the 

gas  in  case  a  gaseous  fuel  is  employed. 
Second,  the  heating  value  of  the  fuel. 

Third,  the  weight  or  volume  of  the  fuel  supplied  to  the  engine. 
Fourth,  the  volume  of  the  air  supplied  to  the  engine. 
Fifth,  the  number  of  revolutions  per  minute. 
Sixth,  the  number  of  cycles  per  minute. 
Seventh,  indicator  cards  are  taken  from  the  cylinders. 
Eighth,  the  weight  of  jacket  water  used,  and  its  initial  and  final 

temperature. 
Ninth,  the  brake  horse-power  of  the  engine. 

The  precautions  which  must  be  taken  in  making  such  a  test  to  insure 
that  the  data  are  properly  taken,  have  been  outlined  by  a  committee 
of  the  A.S.M.E.,  and  the  rules  have  been  published  by  the  society  in 
pamphlet  form.  It  is  important  that  the  conditions  throughout  the  test 
should  be  as  nearly  uniform  as  possible.  Readings  should  be  taken  at 
frequent  intervals,  say  every  ten  minutes. 

A  gas  engine  test  may  be  analyzed  graphically  in  a  manner  similar 
to  that  already  described  in  Art.  195.  The  actual  card  of  the  engine 
is  superimposed  upon  the  theoretical  card  which  would  be  given  were 
the  same  quantriy  of  heat  added  to  a  charge  of  pure  air,  as  was  actually 
introduced  into  the  engine,  per  cycle,  in  the  fuel  used. 

After  determining  the  indicated  horse-power  shown  by  the  different 
sets  of  cards  taken  during  the  test,  that  card  should  be  chosen  whose 
form  and  area  are  nearest  to  the  average.  The  heat  supplied  per  pound 
of  charge  is  next  computed,  and  from  the  dimensions  of  the  engine  and 
the  pressure  of  the  atmosphere  a  theoretical  card  is  drawn.  This  card 


314 


NOTES  ON  INTERNAL  COMBUSTION  ENGINES  ART.  297 


is  shown  in  dotted  lines  in  Fig.  167.  Upon  this  theoretical  card,  to  the 
same  scale  of  pressures  and  volumes,  is  superimposed  the  card  shown 
from  the  test  as  best  representing  the  average  conditions.  Usually  the 
beginnings  of  the  compression  lines  coincide  on  the  two  cards,  since  the 
effect  of  wire  drawing  in  reducing  the  pressure  of  the  charge  at  the 
beginning  of  compression  is  inappreciable.  The  compression  line  of 
the  actual  card  a-c  will,  however,  fall  below  that  of  the  theoretical  card 
a-c'  in  the  manner  shown. 

If  the  charge  were  compressed  to  point  c\1  and  its  combustion  were 
then  instant  and  complete,  the  heat  added  would  raise  the  pressure  to 
some  point  x",  whose  position  may  be  computed.  If  the  charge  then 


FIG.  167. — Graphical  analysis  of  the  losses  in  an  Otto  cycle  engine. 

expanded  adiabatically  following  the  line  x"t" ,  the  engine  would  give  the 
card  Qr-ci-x"-t".  The  difference  between  the  area  x'-t'-t"-x"  and  the  area 
CL-C'-CI  will  then  be  the  power  lost  on  account  of  the  heat  transferred  to 
the  walls  of  the  cylinder  during  the  compression  stroke.  The  area 
ti-x\-x"t"  then  represents  the  work  lost  on  account  of  the  combined 
effects  of  suppressed  combustion  and  heat  loss  to  the  cylinder  wall 
during  the  working  stroke.  Were  the  combustion  not  suppressed,  the 
expansion  line  would  probably  have  approximately  the  form  x"t^.  Were 
there  after  burning  but  no  heat  transfer  to  the  cylinder  wall,  the  expansion 
line  would  have  approximately  the  form  x\t" .  The  available  exhaust 
loss  which  might  be  recovered  by  complete  expansion  of  the  charge, 


ART.  298  ACTUAL  EFFICIENCIES  OF  INTERNAL  COMBUSTION  ENGINES  3 1 5 

is  represented  by  the  area  t-e-a,  which  is  the  power  which  would  be 
obtained  from  the  charge  were  it  expanded  adiabatically  down  to  atmos- 
pheric pressure.  The  remainder  of  the  exhaust  loss  cannot  be  recovered 
by  expansion  of  the  charge.  The^shaded  areas  represent  the  loss  due 
to  fluid  friction,  and  to  the  fact  that  it  takes  an  appreciable  time  for  the 
explosion  pressure  to  reach  its  maximum. 

From  a  complete  internal  combustion  engine  test  a  heat  balance  may  be 
made  out  showing  the  actual  distribution  of  the  heat  supplied  to  the  engine. 
The  proportion  of  the  heat  lost  in  friction  and  that  transformed  into 
useful  work  may  be  readily  computed  from  the  brake  and  the  indicated 
horse-power  of  the  engine.  The  heat  transferred  to  the  jacket  water 
during  the  test  may  be  found  by  measuring  the  water  used  and  obtaining 
its  rise  in  temperature.  The  sensible  heat  rejected  at  the  exhaust  may 
be  found  by  computing  the  temperatures  of  the  charge  at  point  ti  and 
at  point  a  and  multiplying  the  difference  by  the  specific  heat  of  the 
charge  at  constant  volume.  The  remainder  of  the  heat  supplied  is  rejected 
in  the  exhaust  in  the  form  of  unburned  combustible,  or  is  radiated  from 
the  engine,  or  represents  the  error  of  the  test.  It  may  be  noted  that 
the  temperature  of  the  exhaust,  as  obtained  by  a  thermometer,  is  not 
the  temperature  corresponding  to  the  point  TI,  but  is  lower  on  account 
of  the  work  performed  by  the  exhaust  in  expansion  down  to  atmos- 
pheric pressure  against  the  resistance  of  the  air. 

298.  Actual  Efficiencies  of  Internal  Combustion  Engines.  The  total 
efficiency  of  a  good  gas  engine  usually  ranges  between  20  and  30  per 
cent.  Efficiencies  as  high  as  38  per  cent  have  been  claimed,  but  it  is 
very  doubtful  if  total  efficiencies  higher  than  32  per  cent  have  ever  been 
realized.  In  Table  XIV  will  be  found  the  results  of  typical  tests  of 
different  forms  of  internal  combustion  engines.  These  are  not  the 
highest  efficiencies  which  have  been  realized,  but  are  those  which  have 
been  realized  continuously  in  service. 

It  will  be  seen  that  the  efficiency  of  the  internal  combustion  engine 
is  higher  than  that  of  the  steam  engine  or  steam  turbine.  The  cost 
of  fuel  is  therefore  smaller  in  the  case  of  the  internal  combustion 
engine  than  in  the  case  of  a  steam  engine  or  steam  turbine.  The  cost 
of  attendance  is  also  smaller.  On  account  of  the  high  cost  of  an  internal 
combustion  engine  plant,  however,  the  fixed  charges  are  large.  In  units 
of  small  power,  the  cost  of  fuel  and  of  attendance  is  the  principal  item 
of  expense.  In  units  of  large  power  the  fixed  charges  upon  the  invest- 
ment become  the  principal  item.  In  general,  it  will  be  found  that  in 
small  powers,  the  internal  combustion  engine  will  be  the  cheapest  one 
to  operate,  while  in  large  powers  the  steam  plant,  and  more  especially 
the  steam  turbine  plant,  may  be  operated  at  the  minimum  of  expense. 
When,  however,  the  cost  of  fuel  is  high,  as  it  is  in  certain  parts  of  the 


316 


NOTES  ON  INTERNAL  COMBUSTION  ENGINES 


ART.  298 


world,  the  internal  combustion  engine  is  the  prime  motor  of  the  highest 
commercial  efficiency. 

TABLE  XIV 
EFFICIENCIES  OF  MODERN  INTERNAL  COMBUSTION  ENGINES 


Kind  of  Fuel. 

Nominal 
Brake  H.P. 

•a* 

£w 

$(*$ 

F 

3 
O 

-^  ^E 
»  w   . 

go* 

.s1« 

•§fc« 

o 

a; 
j3 

wl 

.Sfe 

go 

w 

Producer 
Efficiency 
Per  Cent. 

J 

<u  . 
0,^ 

t)W 
HPQ 
W 

Mechanical 
Efficiency 
Per  Cent. 

is! 

!!<£ 

H 

Alcohol  

14.0 

1  00 

10,440 

10,440 

24  4 

Illuminating  gas  . 

50.0 

— 

17.75 

560 

—  - 

9,950 

86 

25.0 

Suction  producer  gas  from 
anthracite  

20.0 

0.995 

14,940 

86.5 

12,800 

19  9 

Kerosene  (Diesel  cycle)  .... 

30.0 

0.483 

— 

18,550 

— 

9,000 

72 

28.3 

Blast-furnace  gas  

1200 

— 

— 

— 

— 

9,080 

83.1 

28.1 

Coke  oven  gas  

620 

— 

— 

— 

— 

9,400 

70.3 

27.1 

Producer  gas  

483 

0  .  965 

— 

14,321 

73  .  8 

10,200 

83  .  8 

25.0 

FIG.  168. — Three-cylinder  two-cycle  marine  engine. 


ART.  298     ILLUSTRATIONS  OF  INTERNAL  COMBUSTION  ENGINES     317 

In  Fig.  168  will  be  found  an  illustration  of  a  small  two-cycle  engine, 
using  gasoline  for  fuel,  of  a  type  often  employed  for  propelling  small 
boats.  This  is  a  three -cylinder  engine  with  three  separate  carburetors 
and  jump  spark  ignition,  and  is  governed  by  throttling  the  charge  and 
delaying  the  spark. 

In  Fig.  169  will  be  found  an  illustration  of  a  medium  sized  (50  horse- 
power) four-cycle  stationary  engine,  adapted  for  .operation  with  illumi- 
nating and  natural  gas.  Engines  of  this  type  are  also  frequently  provided 


,*  .. 


FIG.  169. — Four-cycle  stationary  gas  engine. 

with  suction  producer  plants,  and  operate  on  producer  gas  generated  from 
anthracite  coal. 

In  Fig  170  may  be  seen  a  view  of  part  of  an  installation  of  17  gas 
engines,  direct  connected  to  2000  kilowatt  alternating  current  generators. 
This  installation  is  at  the  Geary  plant  of  the  United  States  Steel  Com- 
pany and  the  engines  were  built  by  the  Allis-Chalmers  Company.  The 
engines  are  of  the  four-cycle  type,  operate  on  blast  furnace  gas,  and 
have  four  double  acting  cylinders  each.  By  the  use  of  four  double  act- 
ting  cylinders  in  this  manner,  the  engine  is  made  to  work  with  as  much 
smoothness  as  does  a  cross  compound  steam  engine.  Gas  engines  of  this 
type  have  been  built  of  5400  horse-power. 


318 


NOTES  ON  INTERNAL  COMBUSTION  ENGINES 


Am .  296 


m. 


PROBS.  1-12  PROBLEMS  319 


PROBLEMS 

1.  An  Otto  cycle  engine  having  a  compression  pressure  of  150  Ibs.  gage  is  to  be 
designed.     Assume  atmospheric  pressure  to  be  14  Ibs.  per  square  inch  absolute  and 
atmospheric  temperature  to  be  70°  F.     Find  the  initial  volume  per  Ib.  of  working  fluid. 

Ans.     14.03  cu.ft. 

2.  Find  the  volume  of  the  compression  space  per  pound  of  working  fluid. 

Ans,     2.43  cu.ft. 

3.  Find  the  work  of  compression.  Ans.     68,900  ft.-lbs. 

4.  Find  the  temperature  resulting  from  the  compression.  Ans.     978°  abs. 

5.  Find  the  explosion  pressure.  Ans.     533  Ibs.  per  sq.  in. 

6.  Find  the  terminal  pressure.  Ans.     42  Ibs.  per  sq.  in. 

7.  Find  the  work  of  the  expansion.  Ans.     226,000  ft.-lbs. 

8.  Find  the  net  work  done  per  pound  of  working  fluid.          Ans.     157,100  ft.-lbs. 

9.  Find  the  net  work  done  per  cubic  foot  of  swept  volume.     Ans.     13,550  ft.-lbs. 

10.  The  engine  is  required  to  have  a  nominal  brake  horse-power  of  50.     What 
will  be  the  "required  indicated  horse-power  if  the  nominal  brake  horse-power  is  assumed 
to  be  3/4  of  the  maximum  brake  horse-power?  Ans.     78.5  H.P. 

11.  If  the  engine  makes  75  cycles  per  minute,  find  the  number  of  cubic  feet  of 
swept  volume  per  cycle  required  in  order  to  develop  this  indicated  horse-power. 

Ans.     2.55  cu.ft. 

12.  What  cylinder  diameter  will  be  required-  if  the  piston  speed  is  600  ft.  per  minute, 
and  the  engine  is  single  acting?  Ans.     15^  ins. 


CHAPTER  XXI 
GASEOUS  FUELS 

299.  Classification  of  Fuel  Gases.     The  gases  usually  employed  as 
fuels  may  be  divided  into  six  classes.     They  are: 

1.  Coal  gas. 

2.  Coke-oven  gas. 

3.  Water  gas. 

4.  Natural  gas. 

5.  Producer  gas. 

6.  Blast-furnace  gas. 

Gases  of  the  first  three  classes  are  usually  termed  illuminating  gas, 
since  they  were  originally  made  and  sold  for  lighting  purposes. 

300.  Coal  Gas.     Coal  gas,  often  termed  bench  gas  in  order  to  distinguish 
it  from  by-product  coke-oven  gas,  is  obtained  by  the  destructive  distilla- 
tion of  bituminous  coal,  being  formed  from  the  volatile  matter  of  the  coal. 
In  the  bench  process  the  coal  is  heated  by  means  of  a  coke  fire  in  small 
cast-iron  or  clay  retorts,  holding  two  or  three  hundred  pounds  of  coal 
each.     The   volatile   matter  expelled  from  the   coal   consists  largely  of 
hydrocarbon  vapors  the  greater  part  of  which  are  decomposed  by  the 
heat  into  carbon  and  permanent  gases.     The  substances  evolved  from 
the  coal  are  removed  from  the  retorts  by  means  of  a  pump  termed  an 
exhauster.     They  consist  of  water  vapor,  ammonia,  condensible  hydro- 
carbons and   fixed    gases.      By  cooling  the  products  of  the  distillation 
in  a  suitable  apparatus,  the  water  and  the  condensible  hydrocarbons 
are  removed.     The  gas  is  then  passed  through  a  scrubber  (i.e.,  a  tower 
filled  with  wooden  checker  work,  coke  or  some  similar  material  through 
which  water  trickles).     The  water  in  the  scrubber  absorbs  the  ammonia 
and  removes  the  dust  and  the  final  traces  of  the  condensible  vapors. 
The  gases  are  then  passed  through  purifiers,  which  are  chambers  contain- 
ing trays  of  sesquioxide  of  iron,  or  of  lime,  which  remove  the  sulphur 
compounds  from  the  gases.     The  gas  remaining  is  a  mixture  of  permanent 
gases  consisting  usually  of  from  38  to  48  per  cent  of  hydrogen,  2  to  14 
per  cent  of  carbon  dioxide,  31  to  43  per  cent  of  marsh-gas,  4^  to  7^  per 
cent  of  olefiant  gas  and  1  to  3  per  cent  of  nitrogen.     The  heating  value  of 
the  gas  usually  ranges  from  550  to  650  B.T.U.  per  cubic  foot.     The  prod- 
ucts of  combustion  are,  of  course,  carbon  dioxide  and  water  vapor.     The 

320 


AST.  301  BY-PRODUCT  OVEN  GAS  321 

density  of  the  gas  is  variable,  usually  ranging  from  25  to  50  per  cent  of 
that  of  air.  Coal  gas  is  stored  over  water  in  large  inverted  tanks  called 
gasometers,  and  distributed  to  consumers  by  means  of  pipe  lines.  The 
cost  of  bench  gas  to  small  consumers  usually  ranges  from  $0.80  to  $1.50 
per  thousand  cubic  feet,  and  it  is  occasionally  sold  as  cheaply  as  40 
cents  per  thousand  cubic  feet  to  large  consumers. 

|h  The  by-products  of  the  process  as  well  as  the  gas  itself  have  a  commercial 
value.  The  tar  recovered  from  the  condensing  apparatus  is  a  source  of 
several  thousand  chemicals  of  great  commercial  value,  the  ammonia 
recovered  is  of  value  in  chemical  industries,  and  that  portion  of  the  coke 
not  used  for  heating  the  retorts  is  of  value  as  a  fuel.  However,  'the 
commercial  efficiency  of  the  bench  process  of  gas-making  is  very  low,  and 
it  is  not  profitable  to  use  such  a  gas  as  a  fuel  except  when  comparatively 
small  quantities  of  fuel  are  wanted. 

301.  By-product  Oven  Gas.  Coke  is  in  great  demand  in  the  met- 
allurgical industries.  Formerly  it  was  prepared  in  a  type  of  kiln  usually 
termed  a  bee-hive  coke  oven,  in  which  all  of  the  by-products  resulting  from 
its  manufacture  were  wasted.  It  is  now  often  made  in  a  form  of  oven 
termed  a  by-product  coke  oven,  in  which  the  by-products  resulting  from  its 
manufacture  are  saved  and  utilized.  The  by-product  coke  oven  consists 
of  several  retorts  of  firebrick  placed  side  by  side  in  a  battery.  The  retorts 
are  of  sufficient  size  to  contain  from  6  to  8  tons  of  coal  each.  The  walls 
of  the  retorts  enclose  flues  which  are  heated  by  a  gas  flame.  The 
charging  and  discharging  of  the  retorts .  are  effected  by  machinery. 
Regenerators  are  provided  for  preheating  the  air  and  gas,  used  in  heat- 
ing the  retorts,  so  that  no  heat  is  wasted  by  the  escape  of  hot  gases 
or  products  of  combustion.  In  consequence  of  the  heating  of  the 
retort  the  coal  contained  in  it  is  coked  and  the  volatile  matter  driven  off. 
The  gas  which  first  comes  from  the  oven  is  rich  in  hydrocarbons  and  is 
therefore  suitable  for  illuminating  purposes.  The  gas  which  comes  from 
the  oven  after  the  coking  process  is  nearly  completed  is  deficient  in 
illuminants  on  account  of  the  high  temperature  at  which  it  is  distilled. 
It  is  therefore  suitable  only  for  fuel  gas,  and  a  portion  of  it  is  employed  to 
heat  the  retorts.  The  illuminating  gas  which  comes  from  the  oven  is 
similar  in  character  to  the  gas  obtained  by  the  bench  process,  and  is 
treated  in  a  similar  way  in  order  to  obtain  from  it  the  same  by-products 
and  the  same  quality  of  gas.  The  principal  difference  between  the 
bench  process  and  the  by-product  coke-oven  process  lies  in  the  fact  that 
the  coal  is  handled  in  large  quantities  in  the  latter  process,  that  the  cost 
of  labor  is  very  much  less  and  that  the  value  of  the  coke  produced  is 
much  greater  on  account  of  its  superior  quality.  The  gas  from  a  by- 
product coke-oven  plant  may  be  stored  in  exactly  the  same  way  as  gas 
from  a  bench-process  plant  and  is  suitable  for  exactly  the  same  purposes. 


322  GASEOUS  FUELS  ART.  302 

The  cost  of  making  gas  by  the  by-product  coke-oven  process  is  much 
less  than  by  making  it  by  the  bench  process,  however,  and  it  may  on  that 
account  be  employed  as  a  fuel  when  the  cost  of  bench  gas  would  be 
prohibitive.  By-product  coke-oven  gas  makes  an  ideal  gas-engine  fuel, 
and  the  process  is  especially  suitable  for  use  in  connection  with  a  met- 
allurgical industry  in  which  coke  and  power  are  both  needed. 

302.  Water  Gas.  Water  gas  is  made  by  passing  a  current  of  steam 
through  a  bed  of  incandescent  coke  in  a  suitable  retort.  The  steam  is 
decomposed  to  hydrogen  and  oxygen  and  the  oxygen  unites  with  the  car- 
bon to  form  carbon  monoxide.  The  reaction  is 

C    +   H2O    ==   CO    +   H2 
12  18  28  2 

It  will  be  seen  from  this  reaction  that  in  theory  water  gas  consists  of  eqiml 
volumes  of  carbon  monoxide  and  hydrogen.  By  weight  it  consists  of 
6.67  per  cent  of  hydrogen  and  93.33  per  cent  of  carbon  monoxide.  Its 
heating  value  per  pound  is 

0.933  X 4380  +0.067  X 62,000  =  8230  B.T.U. 

Its  heating  value  per  cubic  foot  will  therefore  be  found  to  be  341  B.T.U. 
Such  gas  is  not  suitable  for  use  as  an  illuminant  in  an  open-flame  burner, 
since  it  burns  with  a  colorless  flame.  Hence,  when  it  is  intended  to  sell 
such  gas  for  illuminating  purposes,  it  is  customary  to  add  to  it  vapors 
obtained  by  the  distillation  of  petroleum  residue,  a  process  termed  enrich- 
ing. These  vapors  are  known  as  illuminants,  and  add  to  the  heating  as 
well  as  the  illuminating  value  of  the  gas. 

The  decomposition  of  the  steam  and  the  consequent  formation  of 
hydrogen  within  the  generator  absorbs  heat.  As  a  result,  the  temperature 
of  the  bed  of  coke  falls,  and  the  reaction  would  soon  cease  if  heat  were 
not  supplied  in  some  manner.  This  is  usually  done  by  passing  a  current 
of  air  through  the  coke  bed  within  the  generator,  by  means  of  which  a 
portion  of  the  bed  of  coke  is  burned  and  the  temperature  of  the  whole 
mass  is  raised.  When  the  temperature  has  reached  a  sufficiently  high 
value,  the  current  of  air  is  stopped  and  a  current  of  steam  takes  its  place. 
As  a  result  of  the  reaction,  the  temperature  of  the  bed  of  coke  is  again 
reduced  until  finally  the  reaction  ceases  and  the  gas  coming  from  the 
producer  consists  principally  of  steam,  instead  of  combustible  gases, 
when  the  current  of  air  is  again  introduced  in  order  to  raise  the  temperature 
of  the  coke.  In  order  to  make  the  water-gas  process  continuous,  it  is 
therefore  necessary  to  employ  two  or  more  generators,  so  that  one  may 
be  warming  up  while  the  other  is  generating  gas.  By  the  employment 
of  a  suitable  regenerator  system,  the  sensible  heat  which  would  be  carried 


ART.  303  NATURAL  GAS  323 

away  in  the  current  of  air  used  to  raise  the  temperature  of  the  coke,  may 
be  saved,  so  that  the  entire  heating  value  of  the  coke  will  finally  appear 
in  the  heating  value  of  the  gas  produced  from  it,  except  for  such  un- 
avoidable losses  as  are  due  to  radiation  and  to  inefficiency  of  the  regen- 
erator system.  It  is  not  usual,  however,  to  employ  a  regenerator  system 
in  small  water-gas  plants,  so  that  the  heating  value  of  the  gas  generated 
from  a  given  quantity  of  coke  is  usually  only  from  50  to  60  per  cent  of 
the  heating  value  of  the  coke. 

Water  gas  is  usually  much  cheaper  than  coal  gas,  and  is  therefore,  of 
more  practical  use  as  a  fuel.  Water  gas,  as  usually  made  and  sold  for 
illuminating  purposes,  after  enriching,  has  a  density  of  0.6  of  that  of  air, 
and  a  heating  value  of  about  600  B.T.U.  per  cubic  foot.  Besides  the 
illuminants,  it  consists  principally  of  carbon  monoxide  and  hydrogen, 
together  with  small  quantities  of  carbon  dioxide  and  nitrogen  and  traces 
of  oxygen  and  other  gases. 

Illuminating  gas  is  now  usually  burned,  when  used  as  an  illuminant, 
in  a  special  form  of  lamp  in  which  the  flame  is  used  to  heat  to  incandescence 
a  fabric  consisting  of  oxides  of  thorium  and  cerium.  The  quantity 
of  light  obtained  by  the  combustion  of  a  given  quantity  of  gas  in  such  a 
lamp  is  many  times  greater  than  would  be  obtained  by  the  combustion 
of  the  same  quantity  of  gas  in  an  open  flame.  The  illuminating  power 
of  the  lamp  depends  only  on  the  heating  value  of  the  gas  and  not  upon 
its  illuminating  power  when  burned  in  an  open  flame.  Illuminating  gas 
companies  are  now  obliged  by  law  in  most  places  to  manufacture  gas 
having  a  given  candle-power  when  burned  in  an  open  flame  under  standard 
conditions.  It  is  to  be  hoped  that  this  requirement  will  speedily  be 
abolished,  since  the  addition  of  illuminants  to  water  gas  is  an  expensive 
process  and  is  of  no  practical  value  at  the  present  time.  Should  the 
candle-power  requirement  be  abolished,  water  gas  could  be  made  and 
sold  at  a  price  which  would  make  it  practicable  to  employ  gas  as  an 
industrial  fuel  for  a  great  many  purposes  for  which  coal  is  now  used. 
For  instance  it  would  then  be  practicable  to  substitute  small  gas  engines 
for  electric  motors  or  isolated  steam  plants,  and  gas  for  electricity  in  the 
illuminations  of  factories,  to  employ  gas  as  a  fuel  in  ovens,  furnaces  and 
forges,  and  even  to  employ  it  for  domestic  heating. 

303.  Natural  Gas.  Natural  gas  is  a  gas  which  is  obtained  from 
petroleum,  bearing  strata  of  rock,  at  considerable  depths  in  the  earth's 
crust.  It  is  obtained  by  drilling  deep  wells,  and  usually  flows  from  porous 
sandstone  rock  saturated  with  petroleum  in  which  the  natural  gas  is 
dissolved  under  pressure.  When  the  pressure  is  relieved  by  the  drill, 
the  gas  evaporates  from  the  liquid  in  which  it  has  been  dissolved  and 
escapes  from  the  openings,  under  a  pressure  ranging  from  a  few  ounces  to 
many  hundreds  of  pounds  per  square  inch.  Natural  gas  consists  almost 


324 


GASEOUS  FUELS 


ART.  304 


304.  Producer  Gas. 

combustion  of  coal  or 


entirely  of  marsh-gas  together  with  traces  of  hydrogen,  hydrocarbons,  car- 
bon dioxide,  oxygen  and  nitrogen.  Its  heating  value  ranges  from  900  to 
1000  B.T.U.  per  cubic  foot.  Its  price  usually  ranges  from  10  to  40  cents 
per  thousand  cubic  feet,  and  it  forms  an  ideal  fuel  when  it  is  available. 
Natural  gas  is  often  transported  long  distances  in  pipe  lines.  The  city  of 
Cleveland,  for  instance,  is  supplied  with  natural  gas  from  West  Virginia. 
The  fall  in  pressure  in  this  long  pipe  line  is  so  great  that  the  gas  must  be 
compressed  to  a  pressure  of  several  hundred  pounds  per  square  inch  before 
delivering  it  to  the  line.  This  is  done  by  means  of  large  gas  compressors 
which  are  driven  by  gas  engines.  The  supply  of  natural  gas,  however, 
seems  to  be  limited,  so  that  it  is  gradually  failing  in  many  fields  and  it  is 
not,  therefore,  a  fuel  of  as  great  commercial  importance  as  might  be 
expected. 

Producer  gas  is  a  fuel  which  is  made  by  the  partial 
coke  with  air  containing  an  excess  of  moisture. 
The  simplest  form  of  apparatus  for  this 
purpose  is  that  illustrated  in  Fig.  171. 
A  is  a  refractory  cylinder  containing  a 
quantity  of  broken  coke  heated  to  incan- 
descence. The  cylinder  may  be  of  steel 
plating  lined  with  firebrick,  or  it  may  be 
a  water-jacketed  cast-iron  cylinder.  At 
the  bottom  of  the  cylinder  there  is 
usually  a  grate  upon  which  the  fuel 
rests.  At  the  top  is  a  hopper  which  is 
closed  by  means  of  a  cone  in  the  manner 
shown.  The  cylinder  is  charged  by  filling 
the  hopper  with  coke  and  then  depressing 
the  cone,  which  allows  the  fuel  to  drop  into 
the  producer,  after  which  the  cone  is  raised 
and  bears  against  the  hopper,  forming  a 

gas-tight  joint.  The  depth  of  fuel  is  usually  from  3  to  5  feet  or  more.  Some 
form  of  blower  or  suction  apparatus  forces  or  draws  air  through  the  fire. 
As  the  air  passes  through  the  lower  layers  of  fuel,  its  oxygen  unites  with 
carbon  to  form  carbon  dioxide.  When  the  oxygen  is  practically  eliminated, 
carbon  monoxide  begins  to  be  formed  by  the  action  of  the  incandescent 
carbon  upon  the  carbon  dioxide,  the  reaction  being 


fTQQpl 


Air  Inlets 

FIG.  171.  —  Diagram   of  a  gas  pro- 
ducer. 


The  gas  which  finally  comes  from  the  fire  therefore  consists  almost  entirely 
of  nitrogen  and  carbon  monoxide,  when  the  air  used  in  blowing  the  pro- 
ducer is  free  from  water  vapor. 


ART.  304  PRODUCER  GAS  325 

Air  consists  of  79.3  per  cent  of  nitrogen  and  20.7  per  cent  of  oxygen 
by  volume.  Each  volume  of  oxygen  becomes  in  the  producer  two  volumes 
of  carbon  monoxide,  so  that  one  volume  of  air  becomes  1.207  volumes  of 

79  3 
producer  gas.     Of  this  producer  gas,  Ty-y  or  65.7  per  cent  by  volume 

is  nitrogen,  which  has  no  heating  value.  The  remainder,  or  34.3  per  cent, 
however,  is  carbon  monoxide,  which  has  a  heating  value  of  338  B.T.U. 
per  cubic  foot  under  standard  conditions  (i.e.,  under  a  pressure  of  one 
atmosphere,  and  at  a  temperature  32°  F).  It  will  be  seen,  then,  that  such  a 
producer  gas  will  have  a  heating  value  of  about  116  B.T.U.  per  cubic  foot. 
In  burning  a  pound  of  carbon  to  CO,  1J  pounds  of  oxygen  or  5.83 
pounds  of  air  are  required  and  4100  B.T.U.  are  liberated.  The  water 
equivalent  of  the  2.33  pounds  of  carbon  monoxide  and  4.50  pounds  of 
nitrogen  formed  as  a  result  of  the  combustion  is  1.67.  The  rise  in  tem- 
perature as  a  result  of  the  combustion  will  therefore  be 


which  will  be  the  approximate  temperature  of  the  gas  coming  from  the 
producer.  This  temperature  is  much  higher  than  is  usual  or  desirable, 
and  the  sensible  heat  of  the  gas  coming  from  the  producer  is  lost  unless 
this  gas  is  used  immediately  for  heating  purposes,  without  cleaning  or 
cooling  it.  The  heat  of  combustion  of  1  pound  of  carbon  is  14,500 
B.T.U.  The  heat  of  combustion  of  the  2^  pounds  of  carbon  monoxide 
formed  from  .this  pound  of  carbon  is  2.33X4380-10,200  B.T.U.  'It 
will  be  seen  that  if  the  gas  is  cooled,  the  efficiency  of  the  producer  will  be 


=  70.3  per  cent. 


In  order  to  increase  the  efficiency  of  the  producer  and  also  in  order 
to  increase  the  heating  value  of  the  gas  formed,  it  is  desirable  to  introduce 
a  quantity  of  water  vapor  with  the  air  which  enters  the  producer.  The 
water  vapor  attacks  the  carbon  in  the  fire,  forming  carbon  monoxide  and 
hydrogen  according  to  the  reaction. 

C    +    H20    =  =    CO    +    H2 
12  18  28  2 

The  effect  of  this  chemical  reaction  is  to  cool  the  fire,  since  the  reaction 
absorbs  heat.  The  quantity  of  water  vapor  admitted  with  the  air  must 
be  so  adjusted  that  the  temperature  of  the  gases  coming  from  the  fire 
shall  be  that  which  will  cause  the  producer  to  operate  in  the  most  efficient 


326  GASEOUS  FUELS  ART.  304 

and  satisfactory  manner.  This  requires  a  temperature  of  about  1800° 
F.,  which  means  that  the  producer  gas  carries  with  it,  as  it  leaves  the  pro- 
ducer, a  considerable  amount  of  sensible  heat.  This  heat  will  be  lost 
unless  it  is  utilized  to  evaporate  the  water  vapor  used  in  the  producer, 
and  to  preheat  the  air  supplied  to  it.  If  the  temperature  of  the  gas 
coming  from  the  producer  could  be  reduced  to  the  temperature  of  the 
external  air,  the  only  loss  which  would  be  sustained  as  a  result  of  the 
operation  of  the  producer  would  be  the  radiation  loss,  which,  by  proper 
design,  may  be  made  very  small.  On  account  of  the  radiation  loss, 
and  the  inefficiency  of  the  regenerative  apparatus  which  must  be 
employed  in  preheating  the  air  and  evaporating  the  water  vapor  used, 
the  efficiency  of  the  producer  cannot  usually  be  greater  than  from  85 
to  90  per  cent,  and  in  most  practical  cases  it  is  below  rather  than  above 
85  per  cent.  Assuming  a  producer  efficiency  of  85  per  cent,  we  will  find 
that  the  heating  value  of  gas  produced  per  pound  of  carbon  burned  will  be 

14,500X0.85=12,300  B.  T.U. 

Assume  that  of  each  pound  of  carbon  burned,  x  pounds  unite  with  the 
oxygen  from  the  air  to  form  air-producer  gas,  and  l-X  pounds  react  with 
steam  to  form  water  gas.  In  forming  water  gas,  1  pound  of  carbon 
forms  Ve  of  a  pound  of  hydrogen,  whose  heating  value  is  10,300 
B.T.U.,  and  2.33  pounds  of  carbon  monoxide,  whose  heating  value  is  10,200 
B.T.U.  The  heating  value  of  the  water  gas  produced  by  1  pound  of 
carbon  is  therefore 

10,300  +  10,200  =  20,500  B.T.U. 

In  forming  air-producer  gas,  1  pound  of  carbon  forms  2|-  pounds 
of  carbon  monoxide,  whose  heating  value  is  10,200  B.T.U.  We  have 
already  seen  that  the  efficiency  of  the  producer  is  such  that  the  heating 
value  of  the  gas  produced  from  1  pound  of  carbon  will  be  12,300  B.T.U. 
Hence  we  may  write  the  equation 

10,200^  +  20,500  (l-X)  =  12,300. 

Solving  this  for  X  we  will  find  that  of  each  pound  carbon  burned  in  the 
producer,  0.796  pounds  unite  with  the  oxygen  of  the  air  to  form  CO,  and 
0.204  pounds  react  with  water  vapor  to  form  CO  and  H.  The  gas  formed 
from  1  pound  of  coke  will  therefore,  consist  of  2  J  pounds  of  CO,  4.50  X 
0.796  =  3.59  pounds  of  nitrogen  and  0.204X^  =  0.035  pounds  of  hydrogen. 
The  volume  of  this  gas  under  standard  conditions  will  be 


0.0781      0.0783       0.00559 


ART.  305    APPARATUS  EMPLOYED  WITH  THE  GAS  PRODUCER  327 

The  heating  value  of  the  gas  per  cubic  feet  will  be 

12,300 


82 


=-450  B.T.U. 


It  will  be  seen  that  the  more  efficient  the  producer  the  larger  will  be  the 
amount  of  hydrogen  and  carbon  monoxide  contained  in  the  gas,  the  less 
the  amount  of  nitrogen,  and  the  higher  the  heating  value  of  the  gas 
per  cubic  foot.  In  practice,  producer  gas  always  contains  a  small  per 
cent  of  CO2  and  a  still  smaller  per  cent  of  free  oxygen. 

305.  Auxiliary  Apparatus  Employed  with  the  Gas  Producer.  The 
air  from  a  producer  may  be  drawn  or  forced  through  the  fire  in  several 
ways.  In  case  the  air  is  supplied  by  means  of  a  steam  blower  or  a  fan, 
the  producer  is  termed  a  pressure  producer.  In  case  it  is  drawn  through 


Scrubber 


FIG.  172. — Suction  gas  producer  plant. 

the  producer  by  the  suction  of  a  gas  engine  or  by  means  of  a  fan,  it  is 
called  a  suction  producer.  In  the  first  case  the  pressure  of  the  gas  in  the 
producer  is  greater  than  that  of  the  atmosphere.  On  account  of  the  great 
depth  of  the  fire  in  the  producer,  a  considerable  difference  of  pressure  is 
usually  required  in  order  to  operate  it,  the  difference  ranging  from  3  to  8 
inches  of  water.  After  the  gas  comes  from  the  producer,  it  must  be 
cleaned  and  cooled  if  it  is  to  be  stored,  or  to  be  used  in  a  gas  engine,  or  to 
be  transmitted  by  means  of  iron  piping.  If,  however,  the  producer  gas 
is  to  be  used  immediately  for  heating,  as,  for  instance,  in  an  open-hearth 
furnace  in  a  steel  works,  it  is  not  necessary  to  clean  and  cool  it.  The 
cleaning  of  producer  gas  is  usually  accomplished  by  passing  it  through 
an  apparatus  termed  a  scrubber,  which  is  a  vertical  cylinder  filled  with 
broken  stone,  coke,  wooden  checker  work  or  something  of  that  kind 
through  which  a  stream  of  water  is  caused  to  trickle.  As  the  current  of 


328  GASEOUS  FUELS  ART.  306 

gas  ascends  through  the  scrubber,  the  action  of  the  wet  surface  is,  of 
course,  to  cool  the  gas,  to  extract  the  dust  and  condensible  vapors  from  it, 
and  finally  to  allow  it  to  escape  at  the  temperature  of  the  entering  scrubbing 
water,  and  in  a  form  suitable  for  use  in  a  gas  engine  or  other  apparatus. 
A  suction  gas  producer  equipped  with  a  scrubber  and  attached  to  a  gas 
engine  is  shown  in  Fig.  172. 

306.  Coal  in  Gas  Producers.  Gas  producers  are  usually  supplied  with 
coal  as  the  fuel  from  which  the  gas  is  made.  The  combustible  in  anthra- 
cite coal  is  nearly  pure  carbon,  and  the  quality  of  gas  made  when  it 
is  used  is  practically  the  same  as  that  which  would  be  made  from  coke. 
However,  one  difficulty  is  encountered  in  the  operation  of  an  anthracite 
gas  producer  which  would  not  be  encountered  in  the  case  of  a  producer 
operated  wfth  pure  carbon.  Anthracite  coal  contains  a  considerable 
percentage  of  ash,  and  in  some  cases  the  ash  is  of  such  a  nature  that  it 
fuses  at  the  temperature  encountered  in  the  producer,  and  forms  a 
vitrified  mass  termed  clinker.  The  presence  of  quantities  of  clinker  has 
a  very  bad  effect  upon  the  operation  of  the  producer.  If  a  coal  is  to  be 
used  which  contains  a  considerable  quantity  of  ash  likely  to  clinker,  the 
producer  must  be  especially  designed  to  permit  of  the  ready  removal  of 
the  clinker  and  so  far  as  possible,  it  must  be  operated  in  such  a  way  as 
to  prevent  its  formation.  A  high  producer  temperature  favors  the  forma- 
tion of  clinker.  The  free  use  of  steam  prevents  the  formation  of  clinker 
by  lowering  the  temperature  of  the  fire,  especially  of  those  parts  of  the 
fire  which  contain  the  largest  proportion  of  ash.  It  is  therefore  necessary 
to  be  liberal  in  the  use  of  steam  if  the  clinker  is  not  to  become  exceedingly 
troublesome. 

In  the  case  of  bituminous  coal,  two  other  difficulties  are  encountered 
in  producer  operation.  The  first  is  due  to  the  fact  that  the  coal  fuses 
in  the  fire,  forming  huge  masses  of  coke  through  which  the  air  cannot  force 
its  way.  It  is  therefore  necessary  to  break  up  the  coke  by  poking  the 
fire  at  intervals  in  the  case  of  a  bituminous  producer.  Bituminous  coal 
sometimes  clinkers,  although  usually  less  trouble  is  encountered  from 
clinkering  in  operating  a  bituminous  producer  than  in  operating  an 
anthracite  producer. 

The  principal  difficulty  encountered  in  operating  a  bituminous  pro- 
ducer comes  from  the  fact  that  the  volatile  matter  which  is  disengaged 
from  the  coal  in  the  producer  consists  very  largely  of  tar  and  condensible 
gases.  If  the  gas  is  to  be  used  immediately  for  heating  purposes,  no  trouble 
results  on  this  account.  If,  however,  the  gas  is  to  be  employed  as  a  gas- 
engine  fuel,  or  if  it  is  to  be  stored  and  distributed  in  iron  pipes,  this  is  a 
serious  matter.  Two  methods  are  available  for  overcoming  this  difficulty. 
The  first  one  consists  in  condensing  the  tar  and  separating  it  from  the 
gas,  as  is  done  in  the  case  of  illuminating  gas.  This  method  is  not  a 


ART.  306 


COAL  IN  GAS  PRODUCERS 


329 


satisfactory  solution  of  the  difficulty,  however,  as  the  separation  of  the 
tar  from  the  gas  involves  a  loss  in  heating  value  and  producer  efficiency, 
and  is  also  an  expensive  process,  since  the  tar  recovered  usually  has  little 
or  no  commercial  value.  A  preferable  method  is  to  cause  the  gases  from 
the  producer  to  pass  through  the  fire  so  that  the  tarry  vapors  are  decom- 
posed into  permanent  gases  by  the  action  of  the  heat  and  steam.  This 
method  is  less  expensive  than  the  mechanical  extraction  of  the  tar,  and 
the  producer  efficiency  is  higher  on  account  of  the  presence  in  the  gas 
of  the  substances  resulting  from  the  decomposition  of  the  tar. 

Two  types  of  producers  are  employed  for  fixing  the  tar.  In  the  first 
type  the  gas  is  taken  from  the  producer  at  or  near  the  hottest  point. 
Such  a  producer  is  shown  in  Fig. 
173.  The  coal  is  introduced  at  the 
top  of  the  apparatus  and  moves 
downward  as  it  burns,  the  ash  being- 
taken  from  the  bottom.  Air  and 
steam  are  introduced  both  at  the 
top  and  at  the  bottom  of  the  pro- 
ducer. The  gas  is  taken  from  an. 
opening  near  the  center  of  the  pro- 
ducer. As  it  moves  downward  through 
the  upper  half  of  the  producer,  the 
fuel  is  coked  and  its  volatile  matter 
distilled.  The  products  of  distillation, 
together  with  steam  and  air,  pass 
downward  through  the  bed  of  incan- 
descent coke  at  the  center  of  the  pro- 
ducer, where  the  action  of  the  heat 
and  of  the  steam  decomposes  the 
tarry  vapors,  transforming  them  into 
permanent  gases. 

In  the  second  type    of   bituminous 
producer     the     apparatus     is    divided 

into  two  or  more  retorts.  The  gases  coming  from  the  first  retort  pass 
through  the  second  retort  before  they  are  taken  to  the  cleaning  apparatus. 
In  such  a  producer  one  of  the  retorts  always  contains  a  fresh  fire.  The 
gases  from  this  retort  contain  an  excess  of  air  and  steam.  On  passing 
into  the  next  retort  they  are  drawn  through  a  bed  of  incandescent  coke. 
The  effect  of  the  heat  and  the  excess  of  air  and  steam  is  to  fix  the  tarry 
vapors,  which  have  been  distilled  from  the  coal  in  the  first  retort.  The 
gases  may  be  then  drawn  through  a  third  or  fourth  retort  in  a  similar 
manner.  One  retort  out  of  the  group  will  usually  be  out  of  commission 
for  the  purpose  of  cleaning  it  and  rebuilding  a  fresh  fire. 


FIG.  173. — Section  of  a  bituminous 
coal  producer  for  the  elimination 
of  tar. 


330  GASEOUS  FUELS  AJRT.  307 

307.  Blast-furnace   Gas.     The  blast   furnace    is    an    approximately 
cylindrical  retort  in  which  iron  ore  is  reduced  by  the  action  of  carbon. 
The  furnace  is  operated  by  filling  it  to  a  considerable  depth  with  hot  coke, 
and  upon  this  bed  of  coke  placing  successive  layers  of  iron  oxide,  lime- 
stone and  coke.     In  passing  through  the  deep  bed  of  coke,  the  air  which 
is  used  to  blow  the  furnace  is  transformed  into  nitrogen  and  carbon 
monoxide.     The   carbon   monoxide   subsequently   reacts   with   the   iron 
oxide  and  is  partially  transformed  into  carbon  dioxide.     The  gas  formed  is 
similar  to  air-producer  gas,  except  that  the  content  of  carbon  dioxide  is 
quite  high.     Blast-furnace  gas  usually  consists  of  about  26  per  cent  of 
carbon  monoxide,  3  per  cent  of  hydrogen,  10  per  cent  of  carbon  dioxide, 
56  per  cent  of  nitrogen  and  about  5  per  cent  of  water  vapor  and  hydro- 
carbons.    Its  heating  value  is  about  98  B.T.U.,  per  cubic  foot.     About 
140,000  cubic  feet  of  blast  furnace  gas  are  produced  for  each  ton  of  iron 
produced  in  the  furnace.     This  amount  of  gas  is  more  than  sufficient  to 
preheat  the  air  admitted  to  the  furnace,  and   to  furnish   all  the  power 
required  by  the  furnace  and  the  steel  plant  usually  associated  with  it.    It 
will  be  seen  that  every  blast  furnace  is  thus  a  source  of  power. 

The  principal  difficulty  encountered  in  the  use  of  blast-furnace  gas  in 
gas  engines  arise  from  the  fact  that  the  gas  is  laden  with  dust  from  the  ore. 
This  dust  is  destructive  to  the  rubbing  surfaces  of  the  cylinder,  and  col- 
lects upon  the  clearance  surface,  causing  pre-ignition  of  the  charge. 
Before  the  gas  is  suitable  for  use  in  a  gas  engine,  the  dust  must  be  removed 
by  the  use  of  fans  and  scrubbers.  Several  types  of  patented  devices  are 
at  present  on  the  market  for  cleaning  blast-furnace  gas,  and  most  of  them 
are  very  efficient.  A  properly  cleaned  blast-furnace  gas  is  an  ideal 
internal  combustion  fuel,  and  engines  using  it  have  given  very  high 
efficiency. 

308.  Other  Fuel  Gases.     Other  fuel  gases  are  used  sometimes  for  special 
purposes  in  the  arts.     For  instance,  acetylene  io  much  used  for  lighting, 
and  in  connection  with  oxygen  for  welding  and  metal-cutting  operations. 
The  cost  of  a  given  quantity  of  heat  when  obtained  by  the  combustion 
of  such  gases  is,  however,  so  much  higher  than  when  obtained  by  the  com- 
bustion  of  ordinary   fuel  gases,   that  they   are  never  employed   except 
when  superior  convenience  or  some  similar  consideration  dictates  their 
use  in  special  cases.     They  are  usually  generated  by  special  processes  from 
comparatively   high  priced   chemicals,   and   the    methods  employed  are 
those  which  are  especially  adapted  for  the  generation  of    small  quanti- 
ties of  gas. 


PUOBS.  1-12  PROBLEMS  331 


PROBLEMS 

1.  Illuminating  gas  having  a  heating  vtfhie  of  600  B.T.U.  per  cubic  feet,  is  sold  at 
$0.80  per  thousand  cubic  feet.     What  is  the  cost  per  million  B.T.U.? 

Ans.     $1.33£ 

2.  What  is  the  cost  per  million  B.T.U.  of  heat  from  coal  having  a  heating  value 
of  13,000  B.T.U.  per  pound,  and  selling  at  $3.50  per  ton  of  2000  Ibs.?     Ans.     $0.1: 1 

3.  Natural  gas  having  a  heating  value  of  1000  B.T.U.  per  cubic  foot  is  sold  at  $0.25 
per  thousand  cubic  feet.     Whatsis  the  cost  per  million  B.T.U.?  Ans.     $0.25 

4.  Producer  gas  having  a  heating  value  of  125  B.T.U.  per  cubic  foot  is  sold  at  6 
cents  per  thousand  cubic  feet.     What  is  the  cost  per  million  B.T.U.?     Ans.     $0.48 

5.  A  gas  producer  employing  pure  carbon  as  a  fuel  has  an  efficiency  of  100  per  cent. 
What  will  be  the  heating  value  of  the  gas  produced  per  pound  of  carbon? 

Ans.   14,500  B.T.U. 

6.  What  proportion  of  the  carbon  reacts  with  the  air  to  form  carbon  monoxide  ? 

Ans.     58.2%. 

7.  What  proportion  reacts  with  the  steam  to  form  carbon  monoxide  and  hydrogen? 

Ans.     41.8%. 

8.  How  many  pounds  of  carbon  monoxide  will  be  formed  per  pound  of  carbon 
burned?  Ans.     2.33  Ibs. 

9.  How  many  pounds  of  hydrogen  will  be  formed  per  pound  of  carbon  burned? 

Ans.     .0697  Ibs. 

10.  How  many  pounds  of  nitrogen  will  be  in  the  gas  produced  per  pound  of  car- 
bon? Ans.     2.59  Ibs. 

11.  What  will  be  the  volume,  of  the  gas  produced  per  pound  of  carbon? 

Ans.     75.2  cu.ft. 

12.  What  will  be  its  heating  value  per  cubic  foot?  Ans.     193  B.T.U. 


CHAPTER  XXII 


COMPRESSED  AIR 

309.  The  Air  Compressor.  Air  under  high  pressure,  as  an  agent  for 
the  transmission  of  power,  has  a  very  wide  application  in  certain  industries, 
notably  in  quarrying,  mining,  and  in  railway  work.  Air  under  high  pressure 
is  usually  termed  compressed  air,  and  is  obtained  by  the  use  of  an  apparatus 
termed  an  air  compressor.  The  type  of  air  compressor  most  usually 
employed  is  that  known  as  a  piston  compressor,  and  consists  of  a  cylin- 
der provided  with  suitable  valves  and  within  which  there  is  a  reciproca- 
ting piston.  The  air  compressor  is  in  effect  a  pump  which  differs  from  an 
ordinary  water  pump  only  in  the  fact  that  it  handles  an  elastic  instead 
of  an  inelastic  fluid.  It  is  therefore  feasible  to  operate  the  air  compressor 
at  much  higher  speeds  than  a  water  pump,  and  it  is  necessary  to.  make 
certain  changes  in  the  design  of  the  mechanism  on  account  of  the  nature 
of  the  fluid  pumped. 

A  section  through  an  air  compressor  cylinder  is  shown  in  Fig.  174. 
As  the  piston  moves  to  the  left,  air  is  drawn  into  the  cylinder  at  atmospheric 

pressure  and  temperature,  through 
the  inlet  valve  I.  When  the  piston 
reaches  the  end  of  its  stroke,  the 
spring  shown  automatically  closes  the 
valve.  During  the  return  stroke  the 
air  undergoes  polytropic  compres- 
sion, but  since  the  amount  of  heat 
transferred  to  the  wall  of  the  cylinder 
(which  is  water-jacketed)  is  small,  the 
compression  is  practically  adiabatic. 
When  the  pressure  of  the  air  in  the 
cylinder  becomes  equal  to  that  in  the 
receiver  into  which  the  air  is  to 
be  discharged,  the  discharge  valve  D 
opens  and  permits  the  air  to  flow 
into  the  receiver.  It  is,  of  course, 

impossible  to  make  an  air  pump  without  any  clearance  volume.  It  will 
therefore  be  seen  that  at  the  end  of  the  discharge  stroke,  the  cylinder 
will  contain  a  small  quantity  of  air  at  high  pressure.  As  the  piston  moves 
forward,  the  pressure  of  this  air  will  hold  the  inlet  valve  closed,  and  it 

332 


FIG.  174. — -Section  of  an  air-compressor 
cylinder. 


ART.  310 


FORM  OF  THE  AIR-COMPRESSOR  CARD 


333 


FIG.  175. — Theoretical  card  from  an  air 
compressor. 


will  expand  adiabatically  to  a  considerable  volume  before  its  pressure 
falls  to  that  of  the  atmosphere.  As  soon  as  the  pressure  falls  to 
atmospheric  pressure,  a  fresh  supply  of  air  will  be  drawn  through  the 
inlet  valve. 

310.  Form  of  the  Air-compressor  Card.  The  form  of  the  card  theoret- 
ically given  by  an  air  compressor  of  the  piston  type  is  shown  in  Fig.  175. 
The  cylinder  is  filled  with  air  at 
atmospheric  'pressure  and  tempera- 
ture at  point  a.  The  line  a-b  repre- 
sents the  adiabatic  compression  of 
the  air.  The  pressure  represented 
by  the  orclinate  to  the  point  b  is  that 
of  the  air  in  the  receiver  into  which 
the  air  is  to  be  discharged.  During 
the  remainder  of  the  compression 
stroke  the  air  is  discharged  at  con- 
stant pressure  as  represented  by 
the  line  b—c.  When  the  piston 
makes  its  return  stroke,  the  air 

contained  in  the  cylinder  at  point  c  expands  adiabatically,  the  expan- 
sion line  being  c-d.  While  the  piston  is  moving  from  d  to  point  a  the 
supply  of  air  for  the  next  stroke  is  being  drawn  through  the  inlet 
valve,  the  line  d-a  being  the  induction  line. 

The  form  of  card  which  would  actually  be  given  by  an  air  compressor 
is  shown  by  the  dotted  lines  in  the  same  figure.     During  the  compression 

period,  on  account  of  the  heat 
lost  to  the  water-jacket,  the  com- 
pression line  falls  somewhat  below 
the  adiabatic  line.  Before  the  air 
can  be  expelled  from  the  cylinder, 
however,  its  pressure  must  rise 
above  that  of  the  receiver,  since  a 
difference  in  pressure  is  necessary 
in  order  to  lift  the  discharge  valve 
against  the  resistance  of  its  springs 
and  to  force  the  air  through  the  con- 
stricted passage  through  which  it 
must  be  delivered .  In  consequence, 
the  actual  discharge  line  lies  above  the  theoretical  discharge  line.  Since 
the  discharge  valve  must  be  opened  quickly  in  order  to  allow  the  air  to 
escape,  an  extra  difference  in  pressure  is  necessaiy  at  first  on  account  of 
the  inertia  of  the  valve.  The  beginning  of  the  discharge  line  therefore 
usually  has  the  form  shown.  In  case  the  weight  of  the  valve  and  the 


FIG.  176. — Effect   of  fluttering  of  valves 
on  an  air  compressor  card. 


334  COMPRESSED  AIR  ART.  311 

strength  of  the  spring  have  a  certain  relation,  the  current  of  air  will  cause 
the  valve  to  vibrate,  which  will  produce  a  series  of  waves  in  the  discharge 
line  as  shown  in  Fig.  176.  During  the  early  part  of  the  suction  stroke, 
while  the  air  contained  in  the  clearance  is  expanding,  it  is  losing  heat  to  the 
water-jacket,  so  that  the  expansion  line  falls  somewhat  below  the  theoreti- 
cal line.  At  the  beginning  of  the  suction  period,  as  at  the  beginning  of 
the  discharge  period,  an  extra  difference  in  pressure  is  needed  in  order  to 
open  the  inlet  valve.  The  suction  line,  therefore,  has  the  form  shown,  and 
in  case  the  relation  between  the  weight  of  the  valve  and  the  strength  of 
the  spring  will  permit  of  it,  the  suction  line  will  also  have  a  series  of  waves 
as  shown  in  Fig.  176.  As  a  result  of  the  friction  of  the  air  in  passing 
through  the  valves  and  of  the  difference  in  pressure  necessary  to  open 
the  valves,  the  work  required  by  the  compression  in  somewhat  greater 
than  that  theoretically  required  to  adiabatically  compress  the  air  and 
deliver  it  to  the  receiver.  In  consequence  of  fluid  friction  and  of  the 
pressure  required  to  open  the  inlet  valves,  the  volume  of  air  taken  into 
the  cylinder,  and  therefore  the  capacity  of  the  compressor,  is  reduced. 
It  is  therefore  advisable  in  designing  compressors  to  so  proportion  the 
valves  as  to  make  the  losses  from  these  sources  a  minimum. 

311.  The  Multi-stage  Compressor.  The  air  which  is  discharged  into 
the  receiver  from  the  cylinder  is  of  high  temperature  on  account  of  its 
adiabatic  compression.  When  this  air  enters  the  piping  system,  it  loses 
heat  by  conduction  and  radiation,  and  shrinks  in  volume.  Since  the  air 
is  subsequently  cooled,  it  will  be  apparent  that  the  heat  imparted  by 
compression  will  be  lost,  and  that  it  will  take  less  work  to  compress 

and  deliver  a  given  volume  of 
compressed  air  if  the  air  is  com- 
pressed isothermally  instead  of 
adiabatically.  Hence,  when  air  is 
wanted  at  high  pressures,  it  is 
usual  to  employ  what  are  termed 
two-stage  compressors  (i.e.,  com- 
pressors in  which  the  air  is  com- 
pressed to  some  intermediate 
pressure  in  a  large  cylinder,  is  then 
-  delivered  to  an  intermediate  re- 


FIG.  177.— Cards  from  a  two-stage  compressor,     ceiver  in  which   it   is    cooled  to 

approximately  its  initial  tempera- 
ture, and  then  compressed  in  a  second  small  cylinder  to  its  final  pressure) . 
When  very  high  pressures  are  required,  three-stage  and  sometimes  four-stage 
compressors  are  employed.  The  cards  which  would  be  given  by  such  a 
compressor  are  shown  in  Fig.  177.  The  adiabatic  compression  line  for  the 
first  cylinder  is  the  line  a-b.  The  discharge  line  for  the  first  cylinder  is 


ART.  312 


THE  WORK  OF  COMPRESSION 


335 


edg 


FIG.  178. — Theoretical  cards  from  a  two- 
stage  compressor. 


the  line  b-c.  The  expansion  and  suction  lines  for  this  cylinder  are  c-d 
and  d-a.  In  consequence  of  the  cooling  which  the  air  undergoes  in  the 
intermediate  receiver,  the  volume  of^the  air  discharged  per  stroke  of  the 
compressor  is  reduced  from  the  volume  represented  by  the  line  c-b,  to 
that  represented  by  the  line  h  e.  In  the  second  cylinder  the  air  is  again 
compressed,  the  compression  line 
e  f  being  practically  adiabatic. 
The  discharge  line  in  the  high- 
pressure  cylinder  is  the  line  /  g, 
and  the  air  contained  in  the 
clearance  space  expands  along 
the  line  g  h.  In  Fig.  178,  a 
theoretical  card  from  a  two-stage 
compressor  without  clearance  is 
superimposed  upon  the  cards 
which  would  be  given  with  adia- 
batic compression  and  with  iso- 
thermal compression.  The  iso- 
thermal compression  line  is  the 
line,  ace  the  adiabatic  com- 
pression line  is  the  line  a  b  g  and  the  theoretical  cards  are  shown  in  full 
lines.  It  will  be  seen  that  the  area  a  b  c  +the  area  c  d  e  is  work  lost  on 
account  of  the  fact  that  the  compression  in  the  cylinders  is  adiabatic 
and  not  isothermal.  Area  c  b  g  d  represents  the  work  saved  by  the 
employment  of  a  two-stage  compressor. 

312.  The  Work  of  Compression.     In  theory,  the  least  quantity  of 
work  necessary  in  order  to  compress  a  given  quantity  of  air  and  to  deliver 

it  into  a  receiver,  is  that  quantity  of 
work  required  to  compress  it  iso- 
thermally.  Referring  to  Fig.  179, 
which  is  the  ideal  card  given  by  an 
air  compressor  without  clearance  and 
having  isothermal  compression,  it  may 
be  seen  that  the  amount  of  work  per- 
formed by  the  air  in  entering  the  cylin- 
der is  represented  by  the  area  o  d  a  a'. 
The  amount  of  work  required  to 
compress  the  air  isothermally  is  that 

represented  by  the  area  6'  b  a  a' .  The  amount  of  work  required  to 
deliver  this  air  into  the  receiver  is  measured  by  the  area  o  ebb'.  Let 
Pa  be  the  pressure  of  the  atmosphere  in  pounds  per  square  foot,  Va 
be  the  volume  of  one  pound  of  air  at  atmospheric  pressure  and 
temperature  and  Pr  the  pressure  of  the  air  in  the  receiver. 


FIG.  179. 


336  COMPRESSED  AIR  ART.  312 

Then  the  work  done  by  the  air  entering  the  cylinder  will  be 

Ua   =  Pa  Va  =  R  Ta,      ......       (1) 

The  ratio  of  compression  will  be 


The  volume  of  the  air  after  compression  will  be 

V 

V,=  ~.  ...     (3) 

The  work  of  compression  will  be 

Uc   =  Pa  Va  log,    T    =   R  Ta  loge  T,   .       .       .        .       .        (4) 

the  work  required  to  deliver  the  air  into  the  receiver  will  of  course  be 
Ud  =  PrVr  =  PaVa  =  Ua       .....     .     (5) 

From  this  it  will  be  seen  that  the  work  required  to  compress  and  deliver 
the  air  will  be 

U  =  Uc+Ud-Ua=PaValo£er  .....     (6) 

from  which  it  may  be  seen  that  the  work  required  to  compress  the  air 
and  deliver  it  is  equal  to  the  work  of  isothermal-  compression. 

The  efficiency  of  compression  of  a  compressor  may  be  defined  as 
the  ratio  of  the  work  theoretically  required  for  isothermal  compression, 
to  the  indicated  work  actually  shown  by  the  cards  from  the  compressor, 
to  be  necessary  to  compress  and  deliver  a  given  quantity  of  air.  It  will 
be  seen  that  the  more  nearly  isothermal  the  compression  is,  the  higher 
will  be  the  efficiency  of  the  compressor.  Since  the  multi-stage  compressor 
approximates  isothermal  compression  more  closely  than  does  the  single- 
stage  compressor,  the  efficiency  of  compression  in  the  case  of  a  multi- 
stage compressor  is  much  higher  than  in  the  case  of  a  single-stage  com- 
pressor. The  efficiency  of  a  compressor  is  also  increased  by  making  the 
valve  passages  of  ample  area  and  so  designing  the  valves  that  the  excess 
pressure  required  to  open  them  is  a  minimum. 

The  work  of  adiabatic  compression  may  be  seen  by  referring  again 
to  Fig.  178.  The  compression  line  may  now  be  assumed  to  be  adiabatic 
instead  of  isothermal.  The  work  done  by  the  air  in  entering  the  cylinders 
is  as  before 

U.  =  P.V.-RT,     .     .     .     .    ,    .     .     (7) 


ART.  313  LOSSES   DUE  TO  CLEARANCE  AND  ALTITUDE  337 

If  Pr  equals  the  pressure  in  the  receiver  against  which  the  air  is  to  be 
discharged,  we  will  have  for  the  volume  of  the  air  at  point  b  a  quantity 
in  which  we  can  designate  by  the  symbol  Vr.  For  its  value  we  will  have 


p  , (8) 

*    » 

The  work  done  in  adiabatically  compressing  the  air  which  is  represented 
by  the  area  b'  b  a  a',  is 


Substituting  the  value  of  Vr  from  equation  (8),  we  have 

'* 


/    L     mi        \ 

V    (P  r  p      r    _  p 

P.-  -^j-  ....     (10) 

The  work  of  delivering  the  air  into  the  receiver  is 

l        r     l 
^rf  ==    *r  •*  r  =    *a  *a    *rr> (11) 

the  net  work  of  adiabatic  compression  will  therefore  be 


r-i 

As  a  usual  thing  the  actual  work  of  compression  will  be  somewhat 
greater  than  this. 

313.  Losses  Due  to  Clearance  and  Altitude.  The  indicated  power  lost 
on  account  of  the  presence  of  air  in  the  clearance  space  of  the  compressor 
at  the  end  of  the  discharge  period  is  inconsiderable  in  amount,  since  the 
air  performs  almost  as  much  work  during  its  expansion  as  was  performed 
upon  it  during  its  compression.  Were  there  no  heat  transfer  to  the  cylinder 
walls,  there  would  be  no  loss  of  power  from  clearance.  However,  the  use 
of  clearance  necessitates  the  employment  of  a  compressor  cylinder  whose 
swept  volume  is  considrably  larger  than  the  volune  of  the  free  air  com- 
pressed per  stroke.  On  account  of  this  increase  in  size  of  the  compressor 
cylinder,  the  friction  loss  in  the  compressor  will  be  larger  and  the  first 
cost  of  the  machine  will  be  greater  than  they  would  be  if  a  cylinder  without 
clearance  were  used.  The  use  of  large  clearance  in  connection  with  an 
air  compressor  is  therefore  undesirable  and  should  be  avoided  as  far  as 
possible. 

The  ratio  of  the  quantity  of  the  free  air  actually  taken  in  per  stroke, 
to  the  swept  volume  of  the  air  compressor  is  termed  the  volumetric 


338  COMPRESSED  AIR  ART.  315 

efficiency  of  the  compressor.  A  high  volumetric  efficiency  is  desirable 
for  the  reasons  already  indicated.  This  is  particularly  the  case  when  the 
compressor  is  to  be  operated  at  high  altitudes.  At  considerable  elevations 
the  pressure  of  the  air  is  much  reduced,  the  pressure  dropping  off  approx- 
imately at  the  rate  of  one-half  pound  absolute  for  each  thousand  feet  in 
elevation  above  the  sea  level.  The  effect  of  this  reduction  in  the  initial 
pressure  of  the  air  is  to  decrease  the  weight  of  a  given  volume  of  free  air, 
and  therefore,  the  decrease  in  volume  of  compressed  air  delivered  by 
each  stroke  of  the  piston.  Consequently  larger  compressors  are  required 
at  high  altitudes  than  at  sea  level,  and  the  volumetric  efficiency  of  the 
compressor  at  high  altitudes  is  less  than  it  is  at  sea  level.  Compressors 
are  usually  rated  by  the  number  of  cubic  feet  of  free  air  which  they  will 
deliver  per  minute  at  normal  speed.  It  is,  not  however,  the  number  of 
cubic  feet  of  free  air,  but  the  number  of  cubic  feet  of  compressed  air  required 
which  determines  the  size  of  the  compressor.  At  high  altitudes,  there- 
fore, it  is  an  important  matter  to  make  certain  that  the  compressor  is 
of  sufficient  capacity. 

314.  Mechanically    Operated    Valves.       When    an     air     compressor 
equipped  with  automatic  valves  is  operated  at  high  speed,  it  becomes 
necessary  to  provide  them  with  rather  stiff  springs,  in  order  to  insure  that 
they  shall  close  promptly  and  avoid  waste  of  air.     The  use  of  such  springs, 
however,  causes  a  waste  of  power  and  a  reduction  in  the  capacity  of  the 
machine,  as  was  seen  when  comparing  the  actual  air  compressor  diagram 
with  the  theoretical  diagram  in  Fig.   175.     The  stiffer  the  springs  with 
which  the  valves  are  equipped,  the  greater  the  difference  in  pressure  which 
will  be  required  in  order  to  cause  them  to  open.     In  order  to  avoid  the 
loss  in  power  and  capacity  resulting  from  the  use  of  automatic  valves, 
the  larger  size  of  air  compressors  are  often  equipped  with  semi-rotary 
valves  similar  to  the  valves  used  in  a  Corliss  engine,  the  inlet  valves  being 
similar  in  form  to  Corliss  exhaust  valves  and  the  discharge  valve  similar 
in  form  to  Corliss  inlet  valves.     In  many  cases  inlet  valves  of  the  Corliss 
type  are  combined  with  automatic  discharge  valves. 

315.  Blowing  Engines.     An  air  compressor  which  delivers  air  under  a 
pressure  of  from  15  to  30  pounds  for  use  in  blast  furnaces  and  steel  works, 
is  usually  termed  a  blowing  engine,  and  the  cylinder  of  such  a  compressor 
is  termed  a  tub.     The  principles  of  operation   of    blowing   engines    are 
the  same  as  those  of  other  air  compressors.     Blowing  engines  are  usually 
fitted  with  mechanically  operated  valves,  instead  of  automatic  valves, 
since  they  are  commonly  operated  at  high  speed  on  account  of  their 
large  capacity.     However,   several  builders  are  now  equipping  blowing 
engines  with  automatic  valves  made  of  thin  sheet  steel  which  are  held 
against  their  seats  by  very  light  springs.     Since  blowing  engines  deliver 
air  against  comparatively  low  pressure,  the  losses  due  to  the  heating  of 


ART.  316  MOISTURE  IN   COMPRESSED  AIR  339 

the  air  by  adiabatic  compression  are  comparatively  small,  and  those  due 
to  fluid  friction  and  the  imperfection  of  the  valve  action  are  comparatively 
large.  Consequently,  blowing  engines  are  made  single  stage,  and  a  great 
deal  of  care  is  taken  in  designing  the  valves. 

316.  Moisture  in  Compressed  Air.     The  principal  difficulties  encoun- 
tered in  the  use  of  compressed  air  arises  from  the  moisture  which  is  con- 
tained in  the  air.     Air  which  is  compressed  to  a  pressure  of  80  pounds 
gage,  is  reduced  to  about  15  per  cent  of  its  former  volume.     Consequently 
a  given  mass  of  it  can  contain  at  a  given  temperature  only  about  15  per 
cent  of  the  moisture  which  it  was  able  to  contain  previous  to  compression. 
Hence  if  the  humidity  of  the  air  is  greater  than  15  per  cent,  some  of  the 
moisture  will  be  deposited  as  water  in  the  receiver  and  piping  system. 
Usually,  from  50  to  80  per  cent  of  the  moisture  contained  in  the  air  is 
deposited  in  the  piping  system  on  this  account  and  it  gives  a  great  deal 
of  trouble,  particularly  in  winter,  from  freezing.     In  order  to  reduce  the 
trouble  from  this  source,  it  is  customary   to   cool  the  air  coming  from 
the  air  compressor,  in  order  that  the  moisture  which  it  contains  may  be 
deposited  in  the  receiver  and  removed  before  the  air  enters  the  piping 
system.     This  process  is  known  as  after-cooling.     In  order  to  reduce  the 
quantity  of  moisture  in  the  air,  and  also  in  order  to  reduce  the  amount  of 
work  required  to  compress  it,  it  is  advisable  to  take  the  supply  of  air 
for  the  compressor  from  the  coolest  point  possible. 

317.  Example   of    Air-compressor   Design.      The    following  example 
will  serve  to  show  the  method  of  calculating  the  size  of  air-compressor 
cylinders.     Assume  that  a  compressor  is  required  which  will  deliver  100 
cubic  feet  of  compressed  air  per  minute  at  a  gage  pressure  of  120  pounds. 
The  normal  pressure  of  the  atmosphere  will  be  assumed  to  be  13  pounds 
per  square  inch  and  the  atmospheric  temperature  to  be  60°.     The  absolute 
pressure  of  compression  will  be  133  pounds  per  square  inch.     The  ratio 
of  the  final  to  the  initial  pressure  will  be  133^13=10.2.     The  number 
of  cubic  feet  of  free  air  required  per  minute  will  therefore  be  1020.     If 
the  compressor  is  to  operate  at  60  revolutions  per  minute,  the  number 
of  cubic  feet  of  free  air  compressed  per  stroke  must  be  8.53.      In  order 
to  equalize  the  work  done  in  the  two  cylinders  of  a  two-stage  compressor, 
the  ratio  of  compression  should  be  the  same  in  each  one.    The  ratio  of  com- 
pression in  each  cylinder  will  therefore  be 


The  pressure  of  the  air  in  the  intermediate  receiver  will  therefore  be 
13X3.2  =41.5  Ibs.     The  volume  of  the  air  will  be 


340  COMPRESSED  AIR  ART.  318 

Assuming  that  the  clearance  volume  of  the  cylinder  is  4  per  cent  of  the 
swept  volume,  we  will  have  for  the  volume  of  the  air  contained  in  the 
cylinder  at  the  beginning  of  the  suction  period,  4-4-0.438=9.14  per  cent 
of  the  swept  volume.  Since  the  total  volume  of  the  cylinder  is  104  per 
cent  of  the  swept  volume,  the  volume  of  the  free  air  taken  in  per  stroke 
will  be  104-9.14=94.86  of  the  swept  volume  of  the  cylinder.  The 
swept  volume  of  the  cylinder  must  therefore  be 

8.53  -f-.  949  =  9  cubic  feet. 

Assuming  the  stroke  of  the  compressor  to  be  4  feet,  the  diameter  of  the 
low-pressure  cylinder  will  be  20^  inches.  In  practice,  this  diameter  would 
be  somewhat  increased. 

With  the  same  ratio  of  compression  and  the  same  clearance  volume 
in  the  high-pressure  cylinder  the  swept  volume  of  the  high-pressure  cylin- 
der will  be  equal  to  the  swept  volume  of  the  low-pressure  cylinder  divided 
by  the  ratio  of  compression.  Consequently,  the  diameter  of  the  high- 
pfessure  cylinder  will  be 


20J  -T-  V32  -  1  1  §  inches. 

The  valves  of  the  compressor  are  usually  designed  so  that  the  nominal 
velocity  of  the  air  passing  through  them  will  be  6000  feet  per  minute. 
In  order  to  prevent  the  cumulative  action  which  would  result  from  the 
heating  of  the  cylinder  wralls  by  the  adiabatic  compression  of  the  air, 
a  water-jacket  must  be  provided.  Were  it  not  for  this  water-jacket, 
the  cylinder  walls  would  become  heated  by  the  air  and  they  in  turn  would 
heat  the  entering  air.  The  adiabatic  compression  of  this  heated  air 
wrould  still  further  heat  the  walls  and  the  result  would  be  that  both  the 
temperature  of  compression  and  the  temperature  of  the  cylinder  walls 
would  increase  together  until  radiation  from  the  walls  would  balance 
the  heat  received  from  the  air.  As  a  result,  a  large  quantity  of  power 
would  be  required  for  the  operation  of  the  compressor,  its  volumetric 
efficienc}^  would  be  seriously  reduced,  and  it  would  be  impossible  to  lubricate 
the  rubbing  parts. 

318.  Flow  of  Air  or  Gas  in  a  Tube.  When  a  fluid  is  caused  to  pass  through  a  tube 
it  is  found  that  a  difference  in  pressure  is  required  at  the  two  ends  of  the  tube  in  order 
to  cause  the  passige  of  the  fluid.  The  amount  of  this  difference  in  pressure  is  usually 
much  greater  than  that  which  is  required  in  order  to  give  the  fluid  the  actual  velocity 
which  it  has  in  the  tube.  We  are  therefore  obliged  to  conclude  that  there  is  a  force 
analogous  to  friction  opposing  the  flow  of  the  fluid,  and  that  the  work  done  by  this 
force  is  transformed  into  heat  and  raises  the  temperature  of  the  fluid.  Experiment 
shows  this  to  be  the  case.  It  further  shows  that  ths  amount  of  this  force  is  proportional 
to  the  length  of  the  tube,  and  to  the  1.8  power  of  the  velocity  of  the  fluid  and  inversely 
proportional  to  the  1.3  power  of  the  diameter  of  the  tube.  It  shows  that  the  force 


ART.  318  FLOW  OF  AIR  OR  GAS  IN  A  TUBE  341 

depends  upon  the  character  of  the  walls  of  the  tube,  and  is  greater  in  the  case  of  tubes 
having  rough  walls  and  less  in  the  case  of  smooth  walls.  It  shows  that  the  force  is 
proportional  to  the  density  of  the  fluid  .and  also  to  a  property  which  we  term  the 
viscosity  of  the  fluid.  Glycerine,  for  instance,  is  not  greatly  denser  than  water,  and  yet 
we  know  by  experience  that  it  is  thicker  or  more  viscous  and  we  find  that  the  force 
of  fluid  friction  is  much  greater  in  the  case  of  glycerine  than  in  the  case  of  water.  We 
may  express  these  observed  facts  by  the  equation 


in  which  dP  is  the  difference  in  pressure  in  pounds  per  square  foot,  between  two  points 
in  a  tube  through  which  a  fluid  is  flowing,  dL  is  the  distance  of  these  points  from  one 
another,  in  feet,  S  is  the  density  of  the  fluid  in  pounds  per  cubic  foot,  v  is  the  velocity 
of  the  fluid  in  feet  per  second,  d  is  the  diameter  of  the  tube  in  feet,  and  A"  is  a  constant 
depending  on  the  character  of  the  interior  surface  of  the  tube  and  also  upon  the  vis- 
cosity of  the  fluid. 

In  the  case  of  a  gas  or  vapor,  the  density  depends  upon  the  temperature  and  pres- 
sure of  the  fluid,  and  since  experiment  shows  that  the  viscosity  of  all  gases  is  prac- 
tically the  same  we  may  write  for  the  above  equation 


dL  -*' 

in  which  P  is  the  pressure  of  the  gas  in  pounds  per  square  foot,  T  is  its  absolute  tem- 
perature, R  is  the  function  T^-m,  and  TV  is  a  factor  which  depends  upon  the  character 

of  the  internal  surface  of  the  tube. 

If  we  let  TF  =  the  number  of  pounds  of  gas  passing  a  given  cross-section  of  the 
tube  per  second,  then  the  volume  of  this  gas  will  be  given  by  the  expression 

V-ZIT..     .     .     .........     (3) 

The  area  of  the  cross-section  of  the  tube  is  equal  to  —  —  .     The  velocity  of  gas  in  the 

tube  is  found  by  dividing  the  volume  of  gas  passing  in  a  given  time  by  the  area  of  the 
tube,  hence  we  may  write 

4/WRT\  , 

(4) 


Raising  to  the  1.8  power  we  will  have 

1'*  R1'9  T*' 


(5) 


Substituting  this  in  equation  (2)  we  have 


¥L  =  K(?^*^-).  > .   /(6) 

Collecting  like  terms  we  will  have 

Integrating  this  expression    between  the  limits  of  Pl  and  P,  and  zero  and  L,  we  will 
have 

>-P-*}=KW"*(?Tr  L,  (8) 


342  COMPRESSED  AIR  ART.  319 

Which  becomes 


- 


in  which  Pl  is  the  initial  pressure  in  pounds  per  square  inch  absolute  at  any  point  in 
the  tube,  P  is  the  pressure  in  pounds  per  square  inch  absolute  at  a  point  L  feet  distant 
from  the  first  point  in  the  direction  of  flow,  W  is  the  number  of  pounds  of  gas  passing 
each  cross-section  of  the  tube  per  second,  d  is  the  diameter  of  the  tube  in  inches,  R 
is  the  density  function  of  the  gas,  T  is  the  absolute  temperature  of  the  gas  and  K  is  a 
constant  depending  upon  the  character  of  the  inner  surface  of  the  tube.  Solving  the 
above  equation  for  the  weight  of  gas  transmitted  per  minute  we  will  have 


1 ~        >  ( 10) 

KL(RTY»    ' 

Solving  for  the  diameter  of  the  tube  required  to  transmit  a  given  weight  of  gas  per 
minute  with  a  given  loss  in  pressure  will  have 


Solving  for  the  value  of  the  constant  when  it  is  to  be  determined,  by  experiment,  we 

will  have 

(P  i-s_  pi-s\  ,74-9 
TT  __  1*1         *      ) a /io\ 

"   Wl-*(R'T)'*L  ' 
The  value  of  K  for  iron  pipes  is  usually  about  0.026. 

319.  Applications  of  Compressed  Air.  Compressed  air  may  be  used 
as  the  working  fluid  in  an  engine,  in  exactly  the  same  way  as  steam  is 
used.  The  card  from  a  compressed-air  motor  is  similar  to  one  from  a 
steam  engine.  The  amount  of  power  given  by  the  air  motor  and  also 
the  weight  of  air  used  may  be  computed  from  the  card.  Since  air  is  a 
permanent  gas,  there  is  no  cylinder  condensation,  and  the  thermal  loss 
with  a  compressed-air  motor  will  be  much  less  than  with  a  steam  engine. 
The  power  developed  from  a  given  weight  of  air  may  be  increased  by  heat- 
ing the  air  before  it  enters  the  motor,  and  if  the  motor  is  to  be  used  con- 
tinuously, it  is  advisable  to  preheat  the  air  in  this  manner.  It  is  usually 
advisable  to  use  air  motors  in  place  of  steam  engines  when  compressed  air 
is  available  and  the  motors  operated  for  only  a  small  portion  of  the  time. 
A  small  steam  engine  is  continually  wasting  heat  when  it  is  not  in  opera- 
tion, and  much  steam  is  wasted  by  cylinder  condensation  in  warming  it 
up  after  each  period  of  idleness.  There  are  ho  such  losses  in  the  case  of 
an  air  motor. 

Compressed  air  finds  its  principal  application  in  quarrying  and  mining, 
in  the  operation  of  rock  drills,  and  channeling  machines.  In  coal  mining 
especially,  it  is  impracticable  to  use  steam  for  operating  such  machines, 
since  the  boilers  must  be  placed  above  ground.  To  transmit  steam  from 
a  boiler  plant  at  the  mouth  of  the  mines,  to  engines  and  drills  situated 


ART.  319  APPLICATIONS  OF  COMPRESSED   AIR  343 

underground  and  hundreds  or  thousands  of  feet  away,  would  result 
in  a  very  great  waste  of  heat  and  in  considerable  danger  to  the  workmen. 
When  compressed  air  is  used  as  the  working  fluid  in  such  machines, 
there  is  no  radiation  of  heat  from  the  piping  or  losses  resulting  from  the 
intermittent  use  of  the  machinery.  Consequently,  if  the  air  compressor 
plant  is  efficient,  the  cost  of  operating  compressed-air  machinery  under 
these  conditions  is  much  less  than  the  cost  of  performing  the  same  work 
by  steam.  Another  field  in  which  compressed  air  is  used  to  great  advantage 
is  in  the  driving  of  percussion  tools  in  shops.  The  pneumatic  riveter 
which  is  usually  employed  in  assembling  structural  work  in  the  field 
is  an  example  of  such  a  tool.  It  consists  of  a  heavy  cylinder  within  which 
a  small,  but  rather  heavy  piston,  termed  a  hammer,  is  caused  to  reciprocate 
by  the  action  of  compressed  air.  A  throttle  valve  is  provided  which 
regulates  the  pressure  of  the  air  admitted  to  the  tool,  and  so  controls 
the  force  of  the  blow.  The  hammer  vibrates  at  a  rate  of  several  hundred 
strokes  per  minute  and  when  provided  with  an  extension  having  a  face 
of  suitable  form,  it  rapidly  batters  the  hot  metal  of  the  rivet  into  shape. 
Since  the  hammer  and  its  extension  are  much  lighter  than  the  cylinder 
in  which  they  are  contained,  the  vibration  of  the  cylinder  is  not  so  excessive 
but  what  it  may  be  held  by  hand  when  in  use.  Similar,  but  lighter  tools 
are  employed  in  foundries  and  machine  shops,  where  they  are  known  as 
pneumatic  hammers.  The  extension  pieces  which  are  attached  to  the 
hammers  are  in  the  form  of  chisels,  calking  tools,  etc. 

In  work  of  this  kind,  while  it  is  desirable  that  the  motors  which  use 
the  air  shall  be  as  economical  as  possible,  it  is  very  much  more  important 
that  they  shall  be  convenient  to  operate,  shall  perform  their  work  rapidly 
and  effectively,  and  shall  be  of  such  rugged  construction  as  not  to  be  injured 
by  hard  usage  and  abuse.  Since  these  conditions  are  often  incompatible 
with  economy,  it  will  be  found  that  rock  drills,  pneumatic  hammers  and 
similar  machinery  are  often  inefficient,  if  we  define  the  efficiency  of  such  a 
piece  of  apparatus  as  the  ratio  of  the  work  which  it  performs  to  the  power 
theoretically  required  to  compress  the  air  which  it  consumes. 

PROBLEMS 

1.  Find  the  quantity  of  work  theoretically  required  in  order  to  isothermally  com- 
press 10  cubic  feet  of  free  air  having  a  pressure  of  14  pounds  per  square  inch  and 
deliver  it  into  a  receiver  in  which  the  pressure  is  70  pounds  per  square  inch. 

Ans.     32,450  ft.-lbs. 

2.  Find  the  work  theoretically  required  to  adiabatically  compress  10  cubic  feet  of 
free  air  having  a  pressure  of  14  pounds  per  square  inch  and  deliver  it  into  a  receiver 
in  which  the  pressure  is  70  pounds  per  square  inch?  Ans.     41,700  ft.-lbs. 

3.  Find  the  efficiency  of  compression  when  the  compression  is  adiabatic? 

Ans.     78%. 


344  COMPRESSED  AIR  PROBS.  4-20 

4.  A  multistage   compressor  compresses  air  having  a  temperature  of  60°  F.  from 
a  pressure  of  14  pounds  per  square  inch  absolute  to  a  pressure  of  56  pounds  per  square 
inch  absolute  in  the  first  stage.     The  air  is  then  cooled  to  60°  F.     In  the  second  stage, 
the  pressure  is  raised  from  56  pounds  to  224  pounds  absolute.     Find  the  work  required 
per  cubic  foot  of  free  air  compressed,  assuming  the  compression  to  be  adiabatic  hi  each 
stage.  Ans.     7110  ft.-lbs. 

5.  Find  the  work  required  assuming  that  the  compression  was  adiabatic  and  was 
completed  in  one  stage.  Ans.     8650  ft.-lbs. 

6.  Find  the  per  cent  of  work  saved  by  the  employment  of  two-stage  compression. 

Ans.     17.8%. 

7.  A  compressor  compresses  air  adiabatically  from  a  pressure  of  14  pounds  absolute 
to  a  pressure  of  84  pounds  absolute.     The  clearance  volume  is  5  per  cent  of  the  swept 
volume.     Find  the  volume  of  the  air  contained  in  the  cylinder  at  the  beginning  of  the 
suction  period,  expressed  as  a  per  cent  of  the  swept  volume  of  the  cylinder? 

Ans.     17.85%. 

8.  Find  the  volumetric  efficiency  of  the  compressor.  Ans.     87.15%. 

9.  Assume  that  the  initial  pressure  in  Problem  7  is  10  pounds  absolute.      Find  the 
volume  of  the  air  contained  in  the  cylinder  at  the  beginning  of  the  suction  period. 

Ans.     22.6%. 

10.  Find  the  volumetric  efficiency  of  the  compressor  under  these  conditions. 

Ans.     82.4%. 

11.  What  must  be  the  swept  volume  of  a  cylinder  having  the  volumetric  efficiency 
obtained  in  Problem  10,  if  it  is  to  deliver  6  cubic  feet  of  free  air  per  stroke. 

Ans.     7.3  cu.  ft. 

12.  Air  having  a  temperature  of  80°  and  humidity  of  70%  is  compressed  from  a 
pressure  of  14.5  pounds  per  square  inch  absolute  to  a  pressure  of  72.5  pounds  per  square 
inch  gage.     What  quantity  of  moisture  will  it  contain  per  cubic  foot  after  compres- 
sion and  cooling  to  the  initial  temperature?  Ans.     .00157  Ibs. 

13.  How  many  cubic  feet  of  free  air  will  be  required  per  cubic  foot  of  compressed 
air?  Ans.     6  cu.  ft. 

14.  How  many  pounds  of  moisture  did  this  quantity  of  free  air  contain? 

Ans.     .00670  Ibs. 

15.  How  many  pounds  of  moisture  are  precipitated  by  the  compression  and  cooling 
of  this  quantity  of  air?  Ans.     .00513  Ibs. 

16.  What  quantity  of  moisture  will  be  precipitated  per  day  in  the  pipe  lines  of  an 
air-compressor  system  compressing  100,000  cubic  feet  of  free  air  per  day,  if  the  con- 
ditions are  those  given  in  Problem  12?  Ans.     513  Ibs. 

17.  Assuming  that  the  clearance  volume  of  the  high-pressure  cylinder  of  the  air 
compressor  in  Art.  317  is  6  per  cent,  what  will  be  the  volume  of  the  air  contained  in 
the  cylinder  at  the  beginning  of  the  suction  period,  in  terms  of  the  swept  volume? 

Ans.     13.7%. 

18.  How  many  cubic  feet  of  air  of  a  pressure  of  41.5  pounds  must  this  cylinder 
handle  per  stroke?  Ans.     2.665  cu.  ft. 

19.  What  must  be  the  swept  volume  of  the  cylinder?  Ans.     2.89  cu.  ft. 

20.  What  will  be  the  diameter  of  the  cylinder?  Ans.     11^  ins. 


CHAPTER  XXIII 

REFRIGERATION 

320.  Refrigerating  Machines.  A  refrigerating  plant  is  an  apparatus 
for  maintaining  a  low  temperature  in  a  desired  region  by  removing 
heat  from  that  region  and  transferring  it  to  a  region  of  high  temperature. 
A  refrigerating  machine  is  the  converse  of  a  heat  engine,  since  it  trans- 
forms work  into  heat,  and  then  rejects  the  heat  into  a  region  of  high 
temperature.  Like  the  heat  engine,  the  refrigerating  machine  employs 
a  working  fluid  and  causes  this  working  fluid  to  undergo  a  thermodynamic 
cycle.  Since  the  object  of  refrigeration  is  the  transfer  of  heat,  and  not 
the  performance  of  work,  it  is  customary  to  take  as  the  efficiency  of  a 
refrigerating  system,  the  ratio  of  the  heat  transferred  to  the  work  done. 
Since  the  mechanical  equivalent  of  the  heat  transferred  is  almost  always 
several  times  as  great  as  the  work  done,  the  efficiency  of  a  refrigeration 
plant  is  usually  greater  than  unity.  A  refrigerating  machine  may  employ 
as  a  working  fluid  either  a  gas  or  a  vapor.  On  shipboard,  air  is  usually 
employed  as  a  working  fluid,  since  the  leakage  of  air  within  the  confined 
space  of  a  ship's  engine  room  is  not  harmful.  In  stationary  plants  the 
vapor  of  ammonia  is  usually  employed  as  the  work  ng  fluid.  Other 
vapors  and  gases  are  also  employed  to  a  considerable  extent. 

Refrigerating  plants  may  be  divided  into  four  classes.  Machines 
of  the  first  class  use  a  permanent  gas  as  their  working  fluid.  After 
being  compressed  and  cooled,  the  working  fluid  is  expanded  adia- 
batically  and  its  temperature  reduced  to  a  low  value.  Machines  of  the 
second  class,  which  are  called  vapor-compression  machines,  liquefy  a  vapor 
by  the  application  of  pressure,  and  by  the  subsequent  re-evaporation  of 
this  liquid  under  low  pressures  the  desired  temperature  is  obta'ned. 
Refrigeration  plants  of  the  third  class  are  termed  absorption  plants. 
In  such  plants  a  volatile  vapor,  like  ammonia,  is  absorbed  by  water  or 
some  other  liquid  and  then  driven  off  under  high  pressure  by  heat  in  such 
a  manner  that  it  may  be  subsequently  cooled  and  condensed.  It  is  then 
evaporated  under  low  pressure,  thus  producing  a  low  temperature.  In 
apparatus  of  the  fourth  class,  a  gas  is  compressed  to  a  very  high  pressure 
and  cooled.  When  it  is  subsequently  expanded  the  work  done  in  separat- 
ing its  particles  against  their  mutual  attractions  lowers  its  temperature 

345 


346 


REFRIGERATION 


ART.  321 


(a  phenomenon  already  referred  to  in  Chapter  III  as  the  Joule-Thomp- 
son effect). 

321.  The  Air -refrigerating  Machine.  A  machine  of  the  first  class, 
using  air  as  a  working  fluid,  is  represented  in  Fig.  180;  In  cylinder 
A  air  is  compressed  adiabatically  and  then  forced  into  the  condenser 
coil  B.  By  its  adiabatic  compression,  its  temperature  is  raised  so  that 
it  is  somewhat  higher  than  the  temperature  of  the  water  supplied  to  the 
condenser.  In  the  condenser,  the  temperature  of  the  air  is  reduced  a 
few  degrees  and  the  air  then  enters  the  smaller  cylinder  C,  where  it  expands 

adiabatically  to  its  original  pressure. 
As  a  result,  its  temperature  is  very 
much  reduced.  It  is  then  discharged 
into  the  coil  D,  usually  termed  a  va- 
porizer, where  it  absorbs  heat  at  low 
temperature  from  the  substance  which 
is  to  be  cooled.  In  this  coil  the 
temperature  of  the  air  is  raised  a  few 
degrees,  and  it  then  enters  cylinder  A, 
where  it  is  again  compressed.  'The 
condenser  B  may  consist  of  a  shell 
filled  with  tubes  through  which  cooling 
water  circulates,  similar  in  its  general 
arrangement  to  a  surface  condenser. 
This  is  the  form  of  condenser  usually 
employed  on  shipboard.  In  stationary 
plants,  the  condenser  usually  consists 
of  a  coil  of  pipe  over  which  water  is 
allowed  to  drip.  By  its  evaporation, 
this  water  cools  the  air  or  other  work- 
ing fluid  contained  in  the  pipes.  The 
vaporizer  may  consist  of  a  coil  of  pipe 
enclosed  in  the  space  to  be  cooled, 

and  it  usually  has  this  form  when  air  is  used  as  the  working  fluid.  When 
ammonia  is  used,  however,  the  vaporizer  pipes  are  usually  immersed  in 
brine,  and  the  cold  brine  is  then  circulated  through  pipes  in  the  space 
to  be  cooled. 

It  will  be  seen  that  the  machine  described  is  an  apparatus  for  cooling 
air  by  expansion,  so  that  it  may  absorb  heat  from  a  cold  body,  and  then 
heating  it  by  compression,  so  that  it  may  reject  that  heat  to  a  hot  body. 
In  practice,  the  temperature  of  the  air  rejected  by  cylinder  A  must  be 
considerably  greater  than  the  temperature  of  the  water  which  cools  it, 
and  the  temperature  of  the  air  exhausted  by  cylinder  C  must  be  quite  a 
little  less  than  the  temperature  of  the  substance  to  be  cooled.  The  cycle 


FIG.  ISO. — Air-refrigerating  machine. 


ART.  322    EXAMPLE  OF  THE  PERFORMANCE  OF  AN  AIR  MACHINE        347 

upon  which  this  machine  operates  is  the  reverse  of  the  Joule  cycle  which 
was  described  in  Chapter  XVIII. 

322.  Example  of  the  Performance  of  an  Air  Machine.  Assume  that 
a  machine  of  this  type  is  required  to  maintain  a  temperature  of  0°  F., 
and  to  reject  heat  at  a  temperature  of  80°  F.  In  order  to  insure  proper 
operation,  we  will  assume  that  a  difference  of  20°  is  necessary  to  effect  the 
heat  transfer  in  each  case,  so  that  the  air  must  be  expanded  until  its 
temperature  is  —20°  F.  or  440°  absolute,  and  must  be  compressed  until 
its  temperature  is  100°  F.,  or  560°  absolute.  We  will  assume  that  the 
cycle  is  performed  with  1  pound  of  air  and  that  the  temperature  of  the 
air  is  raised  10°  in  the  vaporizer.  The  temperature  of  the  air  entering 
the  cylinder  A  will  then  be  450°  absolute.  Assume  that  its  pressure 
is  14.7  pounds  per  square  inch.  The  final  pressure  of  compression  may 
be  found  by  the  formula: 


Solving  we  will  have  for  the  final  pressure 

LA 
560\°-4 


P2  =14.71  j~)      =31.6  Ibs.  per  sq.in., 
\4oO/ 

which  will  be  the  pressure  of  the  air  in  the  condenser.     The  work  done 
during  this  compression  may  be  obtained  by  the  formula 


The  work  done  in  expelling  the  air  into  the  condenser  may  be  found 
by  the  formula 

RT  =53.2X560  -29,900  foot-pounds. 

The  temperature  of  the  air  leaving  the  condenser  will  be 
560X440 


550 


=  54.7.6° 


The  work  which  the  air  does  in  entering  the  cylinder  B  from  the  con- 
denser will  be  equal  to 

53.2X547.6-29,150  ft.-lbs. 
The  work  of  expansion  in  this  cylinder  will  be 

=14,390  ft.-Ibs. 


348  REFRIGERATION  ART.  322 

The  work  of  expelling  the  air  from  the  expansion  cylinder  will  be 

53.2X440  =  23400  ft.-lbs. 
The  work  done  by  the  air  in  entering  the  compression  cylinder  is 

53-2X450  =  23900  ft.-lbs. 

The  net  indicated  work  will  be  found  to  be  447  foot-pounds,  which  is  the 
difference  between  the  work  done  upon  the  air  in  cylinder  A,  and  the 
work  done  by  the  air  in  cylinder  B.  The  heat  transferred  will  be  found 
by  multiplying  the  rise  in  temperature  by  the  specific  heat  of  air  at 
constant  pressure  and  will  be  2.38  B.T.U.  Reducing  this  to  foot-pounds, 
we  will  have  1850  for  the  mechanical  equivalent  of  the  heat  transferred. 
Dividing  the  heat  transferred  by  the  net  indicated  work,  we  will  have 
410  per  cent  for  the  efficiency  of  the  machine.  The  efficiency  of  the 
Carnot  refrigerating  machine  transferring  heat  from  a  region  of  0°  F. 
to  a  region  of  80°  F.  will,  of  course,  be 

T2  460 

T1-T2     540-460 

It  will  be  seen  that  the  efficiency  of  the  reversed  Joule  cycle  is  much  less 
than  the  efficiency  of  the  Carnot  cycle,  although  the  theoretical  efficiency 
obtained  by  the  above  computations  is  considerably  higher  than  would 
be  realized  in  practice.  In  practice,  it  would  be  found  that  neither  the 
expansion  nor  the  compression  of  the  working  fluid  would  be  adiabatic, 
and  in  order  to  obtain  the  temperature  range  desired  a  larger  pressure 
range  would  be  necessary,  which  would  increase  the  amount  of  work 
required  to  operate  the  machine. 

It  will  be  noted  that  less  than  2i  B.T.U.  per  cycle  per  pound  of  work- 
ing fluid  were  transferred  from  the  vaporizer  to  the  condenser.  In 
order  to  transfer  any  considerable  quantity  of  heat  by  means  of  a  refrigera- 
ting machine  operating  on  the  reversed  Joule  cycle,  it  is  necessary  that  the 
machine  be  very  large  and  heavy,  and  on  account  of  the  small  amount  of 
net  work  as  compared  with  the  large  quantity  of  work  performed  in  the 
two  cylinders,  the  mechanical  efficiency  of  the  machine  will  be  very  low. 
In  order  to  reduce  the  size  of  the  cylinders,  it  is  customary  to  keep  the 
air  in  the  vaporizer  at  a  pressure  of  several  atmospheres,  which  greatly 
increases  the  capacity  of  the  machine  without  increasing  its  dimensions. 

Another  type  of  air-refrigerating  machine  operates  upon  the  regenerator  principle. 
The  air  coming  from  the  vaporizer  is  passed  through  a  regenerator,  where  its  tem- 
perature is  increased  almost  to  the  temperature  of  the  condenser.  Its  temperature 
is  then  raised  still  further  by  adiabatic  compression  and  it  enters  the  condenser, 
where  it  is  cooled  somewhat.  It  is  then  passed  through  the  regenerator  in  the  reverse 
direction,  where  it  is  cooled  almost  to  the  temperature  of  the  vaporizer.  It  is  then 


ART.  323 


THE  VAPOR-COMPRESSION  SYSTEM 


349 


expanded  in  a  second  cylinder  and  its  temperature  still  further  reduced  before  it  is 
discharged  into  the  vaporizer.  It  will  be  seen  that  in  the  case  of  such  a  machine, 
the  amount  of  work  performed  upon  the  working  fluid  in  the  first  cylinder,  and  by 
the  working  fluid  in  the  second  cylinder,  *!e  much  less  than  in  the  case  of  the  machine 
previously  described,  although  the  quantity  of  heat  transferred  per  cycle  by  a  given 
weight  of  working  fluid  is  the  same,  when  the  temperature  ranges  of  the  two  cycles 
are  equal.  In  consequence  of  this  fact,  the  regenerator  cycle  offers  certain  practical 
advantages  in  the  matter  of  mechanical  efficiency  and  cost  of  installation. 

323.  The  Vapor-compression  System.  A  vapor-compression  machine 
is  shown  in  principle  in  Fig.  181.  Vapor  (usually  ammonia  vapor) 
is  compressed  in  the  cylinder  A,  and  then  discharged  at  high  pressure 
into  the  condenser  B.  The  temperature  of  the  cooling  water  being  less 
than  the  saturation  temperature  of  the  vapor  at  the  pressure  in  the  con- 


FIG.  181. — Ammonia-compression  plant. 

denser,  the  vapor  gives  up  its  heat  of  superheat  and  then  its  latent  heat  of 
evaporation,  and  so  condenses  to  a  liquid.  After  condensation,  the  liquid 
escapes  through  the  expansion  valve  E  into  the  vaporizer  D,  where  it  evapo- 
rates under  low  pressure  by  abstracting  heat  from  its  surroundings.  The 
pump  A  draws  the  vapor  from  the  cooling  coils  as  fast  as  it  is  formed,  and 
compresses  it  in  order  that  it  may  repeat  its  cycle.  Since  the  temperature 
of  vaporization  in  the  condenser  is  high,  and  since  it  is  low  in  the  vaporizer, 
on  account  of  the  low  pressure,  the  machine  is  able  to  transfer  heat  from 
a  cold  region  to  a  hot  one. 

It  will  be  seen  that  no  work  is  performed  by  the  working  fluid,  so 
that  it  is  evident  that  this  cycle  cannot  be  a  very  efficient  one.  It  has 
the  advantage,  however,  of  being  extremely  convenient  and  of  requir- 


350  REFRIGERATION  ART.  324 

ing  only  a  small  cylinder,  whose  mechanical  efficiency  will  be  compara- 
tively high.  It  is  found  in  practice  that  the  commercial  efficiency  of 
this  type  of  machine  is  superior  to  the  commercial  efficiency  of  the  air 
machine  operating  on  the  reversed  Joule  cycle. 

324.  Example  of  a  Vapor  Compression  Cycle.  In  order  to  illus- 
trate the  action  of  this  cycle,  we  may  take  the  following  example.  The 
working  fluid  is  assumed  to  be  1  pound  of  ammonia.  The  temperature 
range  desired  is  the  same  as  in  Art.  322,  and  we  will  assume,  as  before, 
that  the  fluid  must  be  worked  between  the  temperature  limits  of  100° 
F.  and—  20°  F.  In  order  to  solve  the  prcblem,  it  will  be  necessary  to  make 
use  of  a  table  to  the  properties  of  the  vapor  of  ammonia  which  may  be 
found  in  Peabody's  tables.  The  pressure  of  ammonia  having  a  tempera- 
ture of  —20  F.  is  17.7  pounds  absolute,  which  will  be  the  pressure  of  the 
vapor  in  the  vaporizer.  In  order  to  raise  its  temperature  to  100°,  the 
vapor  must  be  compressed  to  a  pressure  of  210.7  pounds  absolute,  which 
will  be  the  pressure  of  the  ammonia  in  the  condenser.  The  latent  heat 
of  evaporation  of  ammonia  at  a  temperature  of  100°  F.  is  486  B.T.U., 
which  will  be  approximately  the  quantity  of  heat  absorbed  in  condensing 
1  pound  of  ammonia  in  the  condenser.  The  heat  of  the  liquid  at  100°  F. 
is  75  B.T.U.  and  at-  20°  F.  it  is-57  B.T.U.  (i.e.,  57  B.T.U.  will  be 
required  in  order  to  raise  its  temperature  from  —  20°  F  to  32°  F.)  The  latent 
heat  of  evaporation  of  ammonia  at  -20°  F.  is  582  B.T.U.  Of  this  75+ 
57=132  B.T.U.  are  supplied  by  the  heat  of  the  liquid  of  the  ammonia, 
and  the  remainder,  or  450  B.T.U.,  is  absorbed  by  the  vaporizer  from  the 
region  which  is  to  be  cooled.  The  specific  volume  of  ammonia  vapor  at 
-20°  F.,  is  15.  2  cubic  feet,  and  at  100°  F.  is  1.52  cubic  feet.  The  ratio 
of  compression  is  therefore  10,  and  the  work  done,  if  the  compression  is 
assumed  to  be  hyperbolic  is, 

210.7Xl44Xl.52xloge  10-106,000  ft.-lbs., 

which  is  the  mechanical  equivalent  of  136.3  B.T.U.  The  heat  trans- 
ferred is,  of  course,  the  heat  absorbed  by  the  ammonia  in  the  vaporizer 
and  is  450  B.T.U.  The  efficiency  of  the  apparatus  is  then 


450-r-136.3  =  330  per  cent. 

In  theory  the  compression  of  the  ammonia  is  not  hyperbolic.  The 
working  fluid  performs  a  reversed  Rankine  cycle  in  the  compressor  and 
the  amount  of  work  done  can  be  computed  exactly  by  taking  the  difference 
between  the  total  heat  of  1  pound  of  ammonia  vapor  at  a  temperature 
of  100°  and  1  pound  at  a  temperature  of—  20°  F.  The  quality  (or 
superheat)  of  the  vapor  at  100°  may  be  determined  from  its  entropy, 
which  is  the  same  as  its  entropy  at  —20  The  method  of  computing  the 
work  performed  in  the  case  of  this  cycle  will  thus  be  seen  to  be  identical 


ART.  325 


THE  VAPOR-ABSORPTION  SYSTEM 


351 


with  the  method  employed  in  computing  the  work  done  during  a  Rankine 
cycle,  as  described  in  Art.  152.  This  method  is,  however,  much  more 
tedious  and  probably  not  very  much  more  accurate  than  the  assumption 
of  hyperbolic  compression. 

It  will  be  seen  from  the  figures  given  that  the  efficiency  of  the  vapor- 
compression  machine  is  slightly  less  than  that  of  a  machine  operating 
on  the  reversed  Joule  cycle,  but  in  practice,  it  is  found  that  the  mechanical 
efficiency  and  the  capacity  for  a  given  size  of  cylinder  is  so  much  greater 
in  the  vapor-compression  machine  that  the  actual  efficiency  of  the  apparatus 
is  much  greater  than  that  of  the  air-refrigerating  machine. 

325.  The  Vapor-absorption  System.  The  principle  of  the  absorp- 
tion machine  will  be  understood  by  reference  to  Fig.  182.  A  is  a  closed 
cylinder,  termed  the  generator,  partially  filled  with  a  solution  of  ammonia 


Cooling  Water 
to  Absorber , 


^Exhaust  Steam 
from  Pumps 


r 


FIG.  182. — Ammonia-absorption  plant. 


gas  in  water  under  high  pressure.  On  heating  the  generator  by  a  fire  or 
by  steam  coils,  the  ammonia  is  driven  off  through  the  pipe  shown,  into 
the  condenser  B.  Since  the  ammonia  is  under  high  pressure,  it  is  there 
condensed  to  a  liquid  when  cooled  by  the  condensing  water.  The  liquid 
ammonia  comes  from  the  condenser  at  a  temperature  of  perhaps  80°  F., 
and  passing  through  the  expansion  valve  H,  flows  into  the  vaporizer  (7, 
where  it  evaporates.  From  the  vaporizer  the  ammonia  vapor  passes 
through  the  pipe  p  into  a  vessel  d,  which  is  termed  the  absorber,  and  which 
contains  a  solution  of  ammonia.  Brine  is  caused  to  circulate  about  the 
vaporizer  coils  and  is  then  used  to  cool  the  region  whose  temperature 
it  is  desired  to  lower.  The  solution  of  the  ammonia  by  the  water  in  the 
absorber  generates  heat  which  is  carried  off  by  circulating  cooling  water 
through  coils  immersed  in  the  absorber.  The  liquid  contained  in  the 
absorber  is  removed  by  a  pump  and  transferred  to  the  generator  through 


352  REFRIGERATION  ART.  326 

the  regenerator  coil  R.  The  spent  liquid  from  the  generator  is  transferred 
to  the  absorber,  passing  through  this  same  generator  coil  on  the  way. 
The  liquid  entering  the  regenerator  is  thus  heated  while  that  entering  the 
absorber  is  cooled. 

It  will  be  noted  that  the  only  power  required  by  the  absorption  sys- 
tem is  that  required  to  circulate  the  various  liquids  and  to  force  the 
liquid  from  the  absorber  into  the  generator.  It  will  be  seen  that  the 
power  required  is  inconsiderable  as  compared  with  that  required  by  the 
compression  system.  The  amount  of  heat  required  by  the  generator 
is,  of  course,  somewhat  greater  than  the  amount  of  heat  required  to  vaporize 
the  ammonia,  so  that  at  first  sight  it  would  appear  that  this  system  must 
have  an  efficiency  of  less  than  100  per  cent,  which  is  very  low  for  a  refrigera- 
tion system.  However,  the  efficiency  of  the  engine  which  furnishes  mechan- 
ical power  for  the  compressor  in  the  vapor-compression  system  is  rarely 
greater  than  10  per  cent,  so  that  the  efficiency  of  the  absorption  system, 
when  considered  from  the  standpoint  of  the  cost  of  operation  and  not 
of  the  quantity  of  energy  required  to  effect  the  heat  transfer,  is  very  much 
greater  than  that  of  the  compression  system.  The  steam  exhausted  by 
the  pumps  used  in  connection  with  the  vapor-absorption  system  usually 
furnishes  sufficient  heat  to  operate  the  system.  The  amount  of  cooling 
water  taken  by  the  system  is  much  greater  than  that  taken  by  a  vapor- 
compression  plant  of  the  same  capacity. 

326.  Apparatus  for  Liquefying  Gases.  When  very  low  temperature  is 
desired,  as,  for  instance,  when  it  is  desired  to  liquefy  any  of  the  permanent 
gases,  advantage  is  taken  of  the  cooling  which  accompanies  the  expan- 
sion of  the  gas  due  to  the  work  required  to  separate  its  particles 
against  their  mutual  attractions.  The  apparatus  which  is  employed 
to  liquefy  air  is  illustrated  in  principle  in  Fig.  183.  It  usually  consists  of 
3-  or  4-stage  compressor  which  raises  the  pressure  of  the  air  to  from  2000 
to  2500  pounds  per  square  inch.  Next,  this  air  is  cooled  in  the  coil  C 
to  the  lowest  available  temperature,  usually  to  the  temperature  of  the 
coldest  water  available.  In  case  the  Joule-Thompson  effect  of  the  gas 
to  be  liquefied  is  small  at  ordinary  temperatures,  refrigerating  agents  may 
be  employed  to  cool  the  gas  in  this  coil.  After  being  cooled,  it  is  allowed 
to  flow  through  a  long  tube  which  is  enclosed  within  a  second  tube.  At 
the  end  of  this  tube,  the  air  passes  through  the  reducing  valve  V,  and  expands 
into  the  flask  F,  in  which  it  is  proposed  to  collect  the  liquefied  air.  As  a 
result  of  the  expansion,  the  temperature  of  the  air  is  lowered  a  few  degrees. 
This  air  returns  from  the  flask  to  the  compressor  through  the  outside 
tube.  These  two  tubes  act  as  a  regenerator,  and  the  temperature  of  the 
air  coming  to  the  flask  through  the  inner  tube  is  reduced  by  transferring 
its  heat  to  the  cooler  air  returning  to  the  compressor  through  the  outer 
tube.  Since  the  temperature  of  the  air  entering  the  reducing  valve  is 


ART.  327    METHODS   OF  STATING  CAPACITY  AND  EFFICIENCY         353 


lowered  by  the  action  of  the  regenerator,  the  temperature  of  the  air  com- 
ing from  the  reducing  valve  is  lowered  still  further,  and  the  action  is 
cumulative,  the  temperature  of  trTfe  air  being  gradually  reduced  until 
finally  it  becomes  low  enough  so  that  a  portion  of  it  is  liquefied.  After 
passing  through  the  expansion  valve,  a  portion  of  the  liquid  remains 
behind  in  the  flask.  As  soon  as  liquefaction  commences,  no  further 
reduction  in  temperature  takes  place,  but  the  air  continues  to  liquefy, 
and  the  fresh  air,  which  must  be  dried  and  freed  from  carbon  dioxide  in 
order  to  avoid  difficulties  from  the  formation  of  ice  or  carbon  dioxide 
snow  in  the  apparatus,  must  be  taken  into  the  compressor  to  take  the 
place  of  the  air  which  is  liquefied. 

It  will  be  seen  that  the  heat  which  is  extracted  from  the  air  in  cooling 
it  after  compression  is  greater  than  the  work  of  adiabatic  compression 
by  the  amount  of  work  done  by  the  attraction  of  the  particles  of  the  air 


5) 


FIG.  183. — Apparatus  for  liquefying  air. 

while  they  were  being  forced  together;  this  heat  was  transferred  to  the 
cooling  water  from  the  air  which  is  liquefied,  by  the  action  of  the 
regenerator. 

This  type  of  apparatus  is  expensive  and  not  very  efficient,  but  may 
be  employed  to  advantage  when  very  low  temperatures  are  needed  for 
scientific  investigations.  Most  of  the  known  gases  have  been  liquefied 
by  the  employment  of  this  apparatus,  and  there  is  no  reason  to  believe 
that  there  are  any  gases  which  cannot  be  liquefied  in  this  manner  when 
they  can  be  obtained  in  sufficient  quantities. 

327.  Conventional  Methods  of  Stating  Capacity  and  Efficiency.  It 
is  customary  to  rate  refrigerating  machines  by  the  "  ice-melting  effect  " 
in  tons  per  twenty-four  hours.  The  quantity  of  heat  required  for  the 
fusion  of  1  pound  of  ice  is  very  nearly  142  B.T.U.  Consequently  the 
quantity  of  heat  absorbed  by  the  fusion  of  1  ton  of  ice  is  142X2000  = 
284,000  B.T.U,  A  1-ton  refrigerating  machine  or  system  is  then  a 


354  REFRIGERATION  PROBS.  1-10 

machine  or  system  which  is  capable  of  removing  284,000  B  T  U.  per  day 
of  twenty-four  hours  from  the  vaporizer.  Such  a  machine  wiA'l,  in  a  com- 
mercial plant,  usually  be  capable  of  freezing  about  1000  pounds  of  ice 
per  day.  In  comparing  efficiencies  of  refrigerating  machines,  it  is  usual 
to  state  the  ice-melting  effect  in  pounds  in  per  pound  of  coal  or  per  indicated 
horse-power  per  hour,  the  indicated  horse-power  being  the  horse-power 
of  the  engine  which  drives  the  compressor.  Since  the  quantity  of  heat 
transferred  by  a  given  expenditure  of  power  will  vary  with  the  temperature 
range,  being  less  for  large  temperature  ranges  than  for  small  ones,  it  is 
customary  to  state  the  efficiency  for  a  temperature  range  from  0°  F. 
in  the  vaporizer  to  90°  F.  in  the  condenser. 


PROBLEMS 

1.  A  refrigerating  machine  is  required  to  maintain  a  temperature  of  30°  F.  in  a 
region  in  which  condensing  water  is  available  having  a  temperature  of  70°  F.     What 
is  the  maximum  theoretical  efficiency  possible  assuming  a  Carnot  cycle  to  be  employed? 

Ans.     1225%. 

2.  An  air-refrigerating  machine  of  the  type  described  in  Art.  313  is  required  to 
operate  between  the  temperature  limits  given  in  Prob.  1.     Assume  that  the  air  must 
be  cooled  by  expansion  to  10°  F.  and  heated  by  compression  to  90°  F.     If  the  pressure 
of  the  air  in  the  vaporizer  is  50  Ibs.  per  square  inch  absolute,  what  must  be  the 
pressure  of  the  air  in  the  condenser?  Ans.     85.7  Ibs.  per  square  inch. 

3.  Assume  that  the  air  is  warmed  10°  in  the  vaporizer.     How  much  heat  is  trans- 
ferred per  pound  of  air  per  cycle?  Ans.     2.37  B.T.U. 

4.  Find  the  swept  volume  of  the  large  cylinder  per  pound  of  air  per  cycle,  assum- 
ing that  its  volumetric  efficiency  is  80%.  Ans.     4.35  cu.ft. 

5.  A  machine  making  60  revolutions  per  minute  is  required  to  transfer  7200  B.T.U. 
per  hour  from  the  vaporizer.     What  must  be  the  swept  volume  of  the  large  cylinder? 

Ans.     1.84  cu.ft. 

6.  An  ammonia  compression  machine  is  required  to  maintain  the  temperature 
difference  given  in  Prob.  1.     Assume  that  the  temperature  in  the  vaporizer  is  10°F., 
and  the  temperature  in  the  condenser  is  90°  F.     The  pressure  of  ammonia  at  10°  is 
37.8  Ibs.  per  square  inch,  its  specific   volume  is   7.44   cu.ft,   the  heat   of  the   liquid 
is-  24  B.T.U.,  the  heat  of  vaporization  is  558  B.T.U.,  and  the  entropy  of  the  liquid  is 

558 
—0.0501,  and  the  entropy  of  vaporization  is  -   —  .     What  is  the  total  heat  of  the 


vapor  at  this  temperature?  Ans.     534  B.T.U. 

7.  What  is  the  entropy  of  the  vapor  after  compression?  Ans.     1.139 

8.  The  pressure  of  ammonia  at  90°  is  179.6,  the  heat  of  the  liquid  is  64  B.T.U., 
the  heat  of  vaporization  is  494  B.T.U.,  the  entropy  of  the  liquid  is  0,1224,  the  entropy 

494 
of  vaporiaztion  is  -  --  -,  and  the  specific  volume  is   1.76.     What  is  the  entropy  of 

ammonia  vapor  at  90°?  Ans.     1.022. 

9.  Is  the  ammonia  wet  or  superheated  after  compression?        Ans.     Superheated. 

10.  What  quantity  of  heat  is  transferred  from  the  vaporizer  to  the  condenser  per 
pound  of  ammonia  per  cycle.  Ans.     470  B.T.U. 


PROBS.  11-17  PROBLEMS  355 

11.  Assume  that  a  compressor  making  30  revolutions  per  minute  is  required  to 
transfer   1,000,000   B.T.U.  per  hour  from  the  vaporizer  to  the  condenser?      What 
quantity  of  ammonia  must  be  compressed  per  revolution?  Ans.     1.18  Ibs. 

12.  Assuming  that  the  volumetric  efficiency  of  the  compressor  is  80  per  cent,  what 
swept  volume  per  revolution  will  be  required?  Ans.     10.96  cu.ft. 

13.  Assuming  hyperbolic  compression,  what  work,  will  be  required  per  revolution 
to  compress  this  quantity  of  ammonia?  Ans.     75900  ft.-lbs. 

14.  What   will    be     the    horse-power    required   to   drive    the    compressor  if   its 
mechanical  efficiency  is  70  per  cent?  Ans.     98.7  H.P. 

15.  What  is  the  nominal  capacity  of  the  compressor  in  Problem  11? 

Ans.     84.5  tons. 

16.  What  is  the  efficiency  of  the  compressor  expressed  in  pounds  of  ice-melting 
effect  per  indicated  horse-power  per  .hour?  Ans.     71.7  Ibs. 

17.  Assuming  a  coal  consumption  of  3  Ibs.  per  indicated  horse-power  per  hour, 
what  is  the  efficiency  expressed  in  ice- melting  effect  per  pound  of  coal? 

Ans.     23.9  Ibs. 


CHAPTER  XXIV 
HEATING,   VENTILATION,  EVAPORATION,   AND   DRYING 

328.  The  Hygiene  of  Heating  and  Ventilation.  Within  the  human 
body  a  process  of  oxidation  is  continually  going  on.  The  products  of 
oxidation  are  excreted  by  the  lungs  and  the  skin,  and  thrown  off  into  the 
air.  These  products  consist  of  carbon  dioxide  and  water  vapor,  together 
with  other  vapors  or  gases  of  very  small  amount  and  unknown  char- 
acteristics. Carbon  dioxide  was  formerly  thought  to  be  poisonous,  but 
it  is  now  known  that  when  the  air  contains  less  than  1  or  2  per  cent  of  it, 
it  has  no  effect  upon  animal  life,  being  as  inert  as  so  much  nitrogen.  Water 
vapor- is  also  harmless.  We  know,  however  j  both  as  a  result  of  scientific 
investigation  and  practical  experience,  that  the  exhalations  from,  the 
human  body  are  dangerous  to  life,  and  many  authorities  are  of  the  opinion 
that  the  poisonous  exhalations  are  thrown  off  by  the  skin  rather  than  by 
the  lungs.  It  has  been  demonstrated  experimentally  that  when  the 
quantity  of  animal  exhalation  present  in  air  is  great  enough  so  that  the 
carbon  dioxide  content  of  the  air  exceeds  0.07  per  cent,  the  air  is  unfit 
to  breathe.  The  carbon  dioxide  is  not  to  be  regarded  as  an  objectionable 
component,  but  simply  as  an  indicator  which  shows  the  suitability  of  the 
air  for  breathing. 

The  average  adult  requires  about  20  cubic  feet  of  air  per  hour  for 
respiration,  and  exhales  about  0.6  cubic  feet  per  hour  of  carbon  dioxide. 
Since  it  is  impossible  to  avoid  the  mingling  of  the  exhaled  air  and  the 
fresh  air  supplied  by  ventilation,  it  is  necessary  to  furnish  very  much  more 
air  per  person  than  the  20  cubic  feet  actually  consumed.  If  it  be  assumed 
that  the  air  exhaled  from  the  lungs  mingles  freely  with  the  air  supplied 
by  ventilation,  it  is  necessary  to  supply  about  2000  cubic  feet  of  fresh 
air  per  hour  for  each  person  present,  in  order  to  prevent  the  carbon  con- 
tent from  rising  above  0.07  per  cent.  In  old  treatises  on  ventilation 
it  was  assumed  that  the  carbon  dioxide  was  the  dangerous  constituent  of 
the  air,  and  hence  that  an  additional  supply  of  air  was  necessary  in  rooms 
containing  open  flames,  such  for  instance  as  gas  jets.  Since  such  flames 
often  give  off  carbon  monoxide,  sulphur  dioxide,  and  other  objectionable 
gases,  it  is  advisable  to  provide  extra  ventilation  in  such  a  case,  but  this 
extra  ventilation  is  not  made  necessary  by  the  carbon  dioxide.  In  large 
rooms  containing  a  considerable  volume  of  air  per  person  and  which  are 

356 


ART.  328        THE  HYGIENE  OF  HEATING  AND  VENTILATION  357 

used  for  short  periods  only,  as  for  instance,  churches  and  public  halls, 
it  is  not  necessary  to  supply  2000  cubic  feet  of  air  per  person  per  hour, 
since  some  time  will  elapse  before  ttfoair  in  the  room  is  sufficiently  vitiated 
to  require  renewal.  On  the  other  hand,  in  hospitals,  particularly  in  con- 
tagious wards,  it  is  advisable  to  supply  a  much  larger  quantity  of  air 
per  person.  In  the  case  of  dwelling  houses,  with  unpainted  plastered 
walls  and  in  the  case  of  many  other  forms  of  construction  a  considerable 
amount  of  ventilation  is  secured  by  diffusion  through  the  walls  of  the  rooms. 
When  the  composition  of  the  air  in  a  room  having  porous  walls  becomes 
appreciably  different  from  that  of  the  external  air,  diffusion  takes  place, 
which  tends  to  make  the  composition  of  the  air  in  the  room  identical 
with  that  of  the  external  air.  While  this  action  may  be  relied  upon  to 
some  extent  to  supply  ventilation,  it  is  not  a  satisfactory  substitute  for  the 
movement  of  air  in  the  form  of  a  stream  or  current. 

Not  only  is  it  necessary  to  supply  an  adequate  amount  of  fresh  air 
to  effect  the  removal  of  the  organic  exhalations  in  any  inhabited  room, 
but  is  also  necessary  to  keep  the  room  at  a  proper  temperature  and  the 
air  in  the  room  at  a  suitable  humidity.  The  usual  temperature  at  which 
living-rooms  are  maintained  in  America  is  70°  F.  In  Europe  it  is  usual 
to  maintain  living-rooms  at  a  temperature  of  about  60°  F.  Experiments 
in  the  so-called  open-air  schools  and  cold-air  schools  indicate,  however, 
that  in  the  case  of  children  wearing  ordinary  winter  house  clothing 
and  permitted  a  reasonable  degree  of  activity,  that  a  temperature 
between  40°  and  50°  is  the  most  satisfactory  room  temperature.  The 
reason  for  this  is  that  the  exhalations  from  the  body,  on  account  of 
the  relatively  high  temperature,  are  then  sufficiently  lighter  than  the  air 
in  the  room,  so  that  they  rise  promptly  from  the  breathing  zone  and  pass 
out  of  the  room  without  vitiating  the  air  which  the  inhabitants  are  to 
breathe.  Older  persons,  when  engaged  in  sedentary  occupations  and  espe- 
cially those  who  have  been  accustomed  to  warm  living-rooms,  do  not 
find  such  temperatures  agreeable,  however,  and  since  it  is  usually  the 
older  persons  who  determine  such  matters,  the  temperature  of  living- 
rooms  is  usually  maintained  at  a  higher  point  than  proper  hygiene  dictates. 
In  most  schools  at  the  present  time,  68°  F.  is  prescribed  as  the  proper  max- 
imum of  temperature,  and  the  tendency  is  to  lower  this  maximum  rather 
than  to  raise  it. 

The  humidity  of  the  air  supplied  by  ventilation  is  quite  as  important 
a  matter  as  is  its  temperature.  The  normal  humidity  of  out-door  air 
is  about  70  per  cent,  and  this  degree  of  humidity  in  connection  with  a 
temperature  between  60°  and  70°  F.  seems  to  be  most  favorable  to  the 
proper  performance  of  all  the  vital  processes.1 


is  true  only  in  case  the  ventilation  is  unusually  abundant  and  effective. 
When  it  is  not,  a  lower  temperature  is  desirable  in  order  that  the  convection  currents 


358        HEATING,  VENTILATION,  EVAPORTTION,  AND  DRYING    ART.  329 

In  an  artificially  heated  building  it  is  difficult  to  maintain  the  humidity 
of  the  air  at  a  proper  point,  since  the  air  is  taken  into  the  building  at  low 
temperature,  and  therefore  contains  but  a  small  quantity  of  moisture, 
and  its  temperature  is  subsequently  raised  without  increasing  the  moisture 
content.  This  makes  the  air  exceedingly  dry.  The  effect  of  such  dry 
air  upon  the  human  body  is,  of  course,  to  take  moisture  from  the  skin 
and  mucous  membranes  very  rapidly.  This  has  a  tendency  to  make 
the  body  feel  cold  on  account  of  the  rapid  evaporation,  to  produce  diseases 
of  the  nose  and  throat,  and  to  seriously  disturb  the  circulatory  system. 
Hence  if  proper  ventilation  is  to  be  maintained  in  a  building,  it  is  neces- 
sary to  introduce  steam  into  the  air  which  is  to  be  circulated  by  the  venti- 
lating system,  in  order  that  its  humidity  may  be  that  which  is  proper  for 
health. 

329.  Systems  of   Heating.     Two  systems  of  heating  are  employed, 
which  are  known  as  the  direct  and  the  indirect  systems  of  heating.     Direct- 
heating  apparatus  is  apparatus  which  is  placed  in  the  room  to  be  warmed. 
Stoves  and  radiators  are  apparatus  of  this  type.     Indirect  heating  apparatus 
is  apparatus  which  is  employed  to  heat  a  current  of  air  which  is  then 
introduced  into  the  room  to  be  warmed.      Direct-heating  apparatus  is 
employed  principally  in  connection  with  dwelling  houses,  office  buildings 
and  other  places  where  ventilation  is  not  a  matter  of  primary  importance. 
Indirect-heating  apparatus  is  employed  in  schools,  hospitals  and  other 
places  where  adequate  ventilation  is  of  great  importance. 

330.  Direct-heating  Systems.     The  common  coal  stove  is  the  sim- 
plest form  of  direct  heating  apparatus.     It  is  reasonably   efficient,    but 
on  account  of  the  constant  attention  necessary,  and  the  dirt  created  by  the 
use  of  coal  and  the  disposal  of  ash,  the  stove  is  being  displaced  by  other 
forms  of  heating  apparatus  in  which  the  fire  is  maintained  in  a  place  where 
the  handling  of  dirt  and  ash  is  not  objectionable. 

The  most  common  system  of  direct  heating  is  that  which  employs 
steam  as  the  medium  for  distributing  the  heat.  Steam  radiators  con- 
sist of  coils  of  pipe  or  of  shells  of  cast  iron  or  pressed  steel  which  are 
supplied  with  steam  by  piping  from  a  central  boiler  plant.  The  steam 
condenses  within  the  radiator,  transferring  its  heat  to  the  air  in  contact 
with  the  shell.  This  heated  air  rises  and  cold  air  flows  in  to  take  its  place, 
thus  warming  the  air  in  the  room  to  be  heated.  The  condensation  returns 
to  the  boiler  through  the  piping  system.  The  principal  differences 
between  the  several  systems  of  steam  heating  usually  employed  lie  in  the 
method  of  returning  the  condensation  to  the  boiler.  The  simplest  sys- 
tem is  that  illustrated  in  Fig.  184,  amd  is  known  as  the  single-pipe  system. 
In  this  system  a  current  of  steam  ascends  from  the  boiler  B  through  the 

created  by  the  heat  of  the  body  shall  clear  the  breathing  zone  of  undesirable  exhala- 
tions. 


ART.  330 


DIRECT-HEATING  SYSTEMS 


359 


pipe  P  to  the  radiator  R,  and  the  condensation  returns  through  this  same 
pipe  to  the  boiler.  It  will  be  seen  that  it  is  necessary  to  make  the  pipe 
of  ample  size  so  that  the  current  of  steam  will  not  have  a  high  velocity, 
for  if  it  has,  it  will  retard  4,he  returning  current  of  water  and  may  cause 
the  system  to  become  "  water  bound."  It  is  also  necessary  that  the  pipe 
shall  be  so  arranged  that  every  part  of  it  shall  drain  freely  into  the  boiler, 
for  if  a  "  pocket "  is  formed  in  the  pipe  which  can  fill  with  water,  the 
system  will  become  water  bound,  and  the  surging  of  this  water  through 
the  pipes  under  the  action  of  the  steam  will  produce  severe  "  water 
hammer." 


FIG.  184. 


FIG.  185. 


The  return-pipe  system,  illustrated  in  Fig.  185,  provides  a  separate 
pipe  for  the  return  of  the  condensation.  With  this  system,  the  pipes 
may  be  made  smaller  than  with  the  single-pipe  system,  and  pockets, 
although  they  are  to  be  avoided  as  far  as  possible,  are  not  fatal  to  successful 
operation. 

When  a  radiator  system  is  started  up  the  pipes  and  radiators  are  of 
course  full  of  air.  In  order  that  steam  may  fill  the  system,  it  is  necessary 
that  the  air  be  permitted  to  escape.  The  air  usually  escapes  from  the 
radiators  through  valves  termed  air  valves,  which  are  sometimes  automatic 
in  their  action,  but  which  are  usually  of  a  form  requiring  personal  atten- 
tion. If  only  a  part  of  the  air  escapes  from  the  radiator,  those  sections 
of  the  radiator  which  are  filled  with  air  do  not  permit  the  entrance  of 


360         HEATING,  VENTILATION,  EVAPORATION,  AND  DRYING     ART.  330 


\s 


steam,  so  that  only  a  portion  of  the  radiator  will  be  active.  This  is  desir- 
able in  mild  weather,  when  only  a  small  amount  of  heat  is  needed.  The 
principal  objection  to  a  system  of  steam  radiation  is  that  unless  intelligent 
advantage  is  taken  of  the  effect  of  the  presence  of  air  in  the  radiator, 
it  is  necessary  to  leave  the  steam  fully  on  or  to  shut  it  completely  off. 
In  order  to  avoid  this  difficulty  radiators  of  the  form  shown  in  Fig.  186 
are  sometimes  used.  In  these  radiators,  the  steam 
enters  at  the  top,  and  the  condensation  flows  away 
at  the  bottom.  The  steam  enters  the  radiator 
through  the  throttle  valve  V,  which  may  be  opened 
sufficiently  to  admit  the  desired  quantity  of  steam. 
The  air,  being  heavier  than  the  steam,  is  forced  out 
through  the  return  pipe  which  is  connected  into 
the  bottom  of  the  radiator.  A  balance  is  quickly 
established  between  the  quantity  of  steam  supplied 
and  of  steam  condensed,  so  that  air  occupies  the 
bottom  of  the  sections  and  steam  the  top,  and  the 
amount  of  heat  radiated  is  determined  by  the 
amount  of  the  radiating  surface  in  contact  with 
steam. 

The  amount  of  radiating  surface  required  when 
steam  radiation  is  employed  is  usually  determined 
on  the  assumption  that  250  B.T.U.  are  transferred 
per  hour  from  the  steam  to  the  air  by  each  square 
foot  of  radiating  surface.  A  sufficient  amount  of 
surface  is  provided  on  this  assumption,  so  that 
the  amount  of  heat  given  up  by  the  radiators  to  the 

air  in  the  room  is  equal  to  the  amount  of  heat  lost  by  the  room  through 
radiation  and  ventilation. 

In  order  to  estimate  the  amount  of  heat  lost  by  a  room,  it  is  customary 
to  employ  the  formula 


iKrT 

AT 

R 

"3 

LTLT 

t> 

U  D  

\\r 

111/ 

)_Check  Valve 

'IG.  186. 


In  this  equation  H  is  the  number  of  heat  units  required  per  hour  for  heat- 
ing and  ventilating  the  given  room,  c  is  a  factor  varying  from  1.1  to  1.3 
and  depending  on  the  exposure  of  the  room,  the  direction  of  the  prevail- 
ing winds  etc.,  G  is  the  number  of  square  feet  of  glass  surface  in  the 
windows,  W  is  the  number  of  square  feet  of  wall  surface  exposed  to  out- 
door air,  n  is  the  number  of  air  changes  required  per  hour  for  ventilation, 
C  is  the  number  of  cubic  feet  of  air  space  in  the  room,  T\  is  the  temperature 
at  which  the  room  is  to  be  maintained,  and  To  is  the  lowest  outdoor  tem- 
perature which  it  is  desirable  to  provide  against. 


ART.  331 


EXHAUST-STEAM  HEATING 


361 


The  following  example  will  serve  to  show  the  method  of  computing 
the  amount  of  radiating  surface  which  will  be  required  in  a  given  room. 
Assume  a  room  30  feet  long,  20  feet  wide,  and  15  feet  high  having  a  side 
and  an  end  wall  exposed  to  the  external  air.  Assume  that  the  room  is 
provided  with  four  windows,  which  are  each  4  feet  wide  and  10  feet  high, 
and  that  it  is  to  house  40  persons.  The  number  of  cubic  feet  of  air 
required  per  hour  will  be  40X2000X80,000,  which  is  the  value  of  n  C 
in  the  formula.  The  value  of  G  in  the  formula  will  be  4X4X10  =  160 
square  feet  of  window  surface.  The  value  of  W,  the  exposed  wall  surface, 
will  be  (15X20 +  15X30) -160 -590  square  feet.  The  value  of  c  we 
will  assume  to  be  1.2  and  we  will  also  assume  that  the  room  is  to  be  main- 
tained at  the  temperature  of  70°  when  the  temperature  of  the  external 
air  is  zero.  We  will  then  have  for  the  number  of  heat  units  per  hour  for 
heating  and  ventilating  the  room 


70-126,000. 


For  the  number  of  square  feet  of  radiating  surface  needed  we  will  have 

126,000 


To 
Radiators  - 


331.  Exhaust-steam  Heating.  When  exhaust  steam  from  an  engine 
is  available,  it  may  be  used  for  heating.  In  office  buildings  it  is 
customary  to  install  a  plant  in  which  steam  engines  are  used  for 
furnishing  light  and  power  for 
the  building  and  the  exhaust 
steam  is  employed  for  heating. 
The  engine  usually  exhausts  into 
a  tank  or  header,  to  which  the 
piping  system  is  connected,  as 
shown  in  Fig.  187.  The  header 
is  provided  with  a  relief  valve  R, 
whose  purpose  it  is  to  allow  the 
escape  of  steam  when  its  pressure 
exceeds  a  certain  value.  The 
steam  passes  from  the  header  to 
the  heating  system,  and  so  long 
as  the  amount  of  steam  supplied 
by  the  engine  is  great  enough,  FIG.  187. 

the    excess  will    escape    through 

the  relief  valve.  When  the  amount  of  steam  supplied  by  the  engine 
is  not  sufficient  to  heat  the  building,  steam  enters  the  header  from 
the  boiler  through  the  pressure-reducing  valve  V.  If  the  relief  valve 


362         HEATING,  VENTILATION,  EVAPORATION,  AND  DRYING     ART.  332 


be  set  to  operate  at  3  pounds  gage,  while  the  pressure-reducing  valve  is 
set  to  operate  at  2  pounds  gage,  it  will  be  seen  that  the  tank  will  always 
contain  steam  at  a  pressure  of  between  2  and  3  pounds. 

In  some  systems,  termed  vacuum-heating  systems,  the  air  is  removed 
from  the  system  by  means  of  a  vacuum  pump  or  a  steam  jet  and  the 
pressure  of  the  steam  within  the  system  is  maintained  at  some  value 
less  than  atmospheric  pressure.  The  advantage  of  this  system  of  opera- 
tion is  that  it  reduces  the  quantity  of  steam  required  by  the  engine.  It 
is  especially  adapted  to  those  cases  where  the  amount  of  steam  exhausted 
by  the  engine,  when  operated  under  high  back  pressure,  would  be  greater 
than  the  amount  of  steam  required  for  heating  purposes.  With  this  type 
of  heating  plant,  it  is  important  that  the  system  be  made  air-tight  by 
carefully  making  all  joints  and  packing  the  valves  so  that  the  quantity 
of  air  to  be  handled  by  the  vacuum  pump  will  be  a  minimum. 

332.  Hot-water  Heating.  A  system  of  direct  radiation  often  used 
in  domestic  heating  is  known  as  hot-water  heating.  In  this  system  water 
is  heated  in  an  apparatus  similar  to  a  boiler,  termed 
a  heater.  The  water  is  caused  to  circulate  through 
radiators,  and  after  being  cooled,  is  returned  to  the 
heater.  The  circulation  is  produced  by  the  difference 
in  the  density  of  the  hot  water  coming  from  the 
heater  and  the  cold  water  which  has  passed  through 
the  radiators  and  is  returning  to  the  heater.  A  hot 
water  plant  is  shown  in  principle  in  Fig.  188.  H  is 
the  heater,  which  is  located  at  the  lowest  point  in 
the  system  and  R  is  the  riser  which  supplies  the 
radiators  with  hot  water.  This  riser  terminates  in  a 
tank,  E,  termed  the  expansion  tank.  The  purpose  of 
this  tank  is  to  permit  the  expansion  of  the  water 
without  allowing  it  to  escape  from  the  system.  Since 
the  water  in  the  riser  R  will,  on  account  of  its  tem- 
perature, be  lighter  than  the  water  in  the  return  pipe 
P,  it  will  flow  through  the  radiators,  surrendering  its 
heat  to  the  air  in  contact  with  them.  By  partially 
closing  the  valve  which  supplies  the  water  to  the 
radiator,  the  amount  of  heat  radiated  may  be 
controlled,  which  is  a  great  advantage  in  house- 
heating  in  mild  weather.  Since  the  temperature  of 
the  water  in  the  radiator  averages  much  lower  than 
the  temperature  of  the  steam  ordinarily  supplied  to 

radiators,  it  will  be  seen  that  a  large  radiating  surface  is  necessary.  It  is 
usual  to  assume  that  1  square  foot  of  hot  water  radiation  will  supply 
180  B.T.U.  per  hour  to  the  room  in  which  it  is  situated. 


FIG.  188. 


ART.  334 


INDIRECT  HEATING 


363 


333.  Indirect  Heating.     Two  systems  of  indirect  heating  are  in  use. 
In  the  first  system  the  difference  in  density  between  the  hot  air  in  the 
ventilating  flues  and  in  the  cold  air  in  the  building,  is  depended  upon  in 
order  to  circulate  the  air  required  for  ventilation;  in  the  second  system 
a  fan  or  other  mechanical  impeller  forces  the  air  to  the  proper  point. 
The  hot-air  furnace  employed  in  heating  dwelling  houses  is  an  example  of 
the  first  method.     Such  a  heating  system  is  illustrated  in  principle  in  Fig. 
189.     The  hot-air  furnace  is  placed  at  some  point  lower  than  the  lowest 
point  which  it  is  required  to  heat.     The  air  is  warmed  by  a  fire  which  is 
separated  from  it  by  a  partition,  usually  of  cast  iron.     The  air  is  carried 
by  flues  to  the  rooms  to  be  warmed.     Since  the  warm  air  in  the  flues  is 
lighter  than  the  air  in  the  rooms,  the  air 

in  the  rooms  descends  to  the  basement, 
where  it  enters  the  furnace  and  rises 
through  the  flues  and  registers.  When 
the  furnace  draws  its  supply  of  air  to  be 
warmed  from  the  basement  itself,  the 
air  in  the  house  is  not  renewed.  If, 
however,  the  furnace  draws  a  part  or 
all  of  its  supply  of  air  from  out  of 
doors  through  a  "  cold  air  box,"  and 
the  air  in  the  house  is  allowed  to 
escape  instead  of  being  returned  to 
the  basement,  ventilation  is  secured. 
In  public  buildings  where  large  num- 
bers of  people  congregate,  it  is  unde- 
sirable to  recirculate  the  air,  since  the 
demands  of  ventilation  are  such  that, 
if  the  air  were  used  over  again,  it  would  JTIG|  i§9. 

be  too  foul.     In  the  case    of   dwelling 

houses,  however,  on  account  of  the  small  number  of  inhabitants  as 
compared  with  the  radiating  surface  of  the  house,  it  is  desirable  to 
recirculate  a  large  part  of  the  air  used,  in  order  to  conserve  heat. 

When  large  buildings  are  to  be  heated  and  ventilated,  indirect  steam 
heating  is  often  employed.  In  this  system,  steam  coils  or  radiators  of 
special  form  are  placed  in  the  ventilating  flues,  at  a  point  below  the  level 
of  the  floor  of  the  room  to  be  warmed.  Since  the  air  in  the  flue  is  highly 
heated  by  the  radiator,  it  rises  into  the  room,  forcing  out  the  cold  foul 
air  which  the  room  contains.  On  account  of  the  vigorous  air  circulation 
and  the  form  of  radiator  usually  employed,  a  square  foot  of  indirect  radiat- 
ing surface  will  impart  400  B.T.U.  per  hour  to  the  air  passing  it. 

334.  Forced     Ventilation.     In    the    ventilating    systems    previously 
described,   dependence  was  placed  upon  the  difference  in  temperature 


364         HEATING,  VENTILATION,  EVAPORATION,  AND  DRYING     ART.  334 


between  the  air  in  the  ventilating  flues  and  the  air  in  the  building  in  order 
to  secure  a  proper  circulation.  However,  since  weather  conditions  will 
often  destroy  the  effectiveness  of  such  a  system,  it  is  advisable  where 
adequate  ventilation  is  essential  under  all  weather  conditions,  to  install 
some  mechanical  device,  such  as  a  fan,  for  moving  the  air,  in  order  to 
insure  that  a  sufficient  quantity  of  it  shall  be  moved  to  the  places  where 
it  is  needed.  Such  a  system  of  mechanical  ventilation  is  illustrated  in 
Fig.  190.  A  boiler  B  supplies  steam  to  coils  of  pipe  placed  in  the  ventilat- 
ing duct  D.  A  fan  F  supplies  the  air  used  for  ventilation.  Through  the 
jets  J  the  steam  is  introduced  to  properly  humidify  this  air  after  it  has 


Room 


[ ( I I 


FIG.  190. 

been  warmed.  The  air  rises  through  the  duct  to  the  room  which  is  to  be 
heated.  The  best  method  of  distributing  the  air  in  the  room  is  still  an 
open  question.  It  would  be  natural  to  introduce  the  warm  air  at  the  top 
of  the  room  and  to  allow  it  to  expel  the  cool  air  at  the  bottom  of  the  room. 
Since,  however,  the  exhalations  from  the  body  are  warmer  than  the  air 
contained  in  the  room,  they  would  tend  to  rise  and  then  to  be  forced 
down  again  into  the  breathing  zone  by  the  down-coming  and  slow-moving 
current  of  air  from  above.  The  best  method,  (which,  however,  is 
quite  expensive  in  application)  is  to  admit  the  air  at  the  bottom  of  the 
room  in  the  manner  shown,  so  that  it  is  uniformly  distributed  to  all  parts 
of  the  room.  The  foul  air  is  removed  at  the  top  of  the  room.  If  incom- 


ART.  335 


EVAPORATION 


365 


ing  air  were  supplied  at  localized  points,  as  it  would  be  if  supplied  through 
registers,  the  fresh  air  would  immediately  rise  to  the  top  of  the  building 
and  there  escape,  leaving  the  foul  air  behind.  By  distributing  it  through 
very  numerous  small  openings,  spaced  uniformly  over  the  entire  floor 
area,  this  difficulty  may  be  avoided. 

In  some  cases  it  is  desirable  that  the  air  introduced  into  a  building  shall 
be  free  from  dust.  This  is  especially  the  case  in  hospitals,  since  dust  acts 
as  a  germ  carrier.1  The  removal  of  dust  is  accomplished  by  passing  the 
air  through  a  scrubber  or  other  form  of  gas-washing  apparatus  before  the 
air  is  heated. 

335.  Evaporation.  In  many  of  the  chemical  industries  it  is  neces- 
sary to  evaporate  solutions  of  salts  in  order  to  obtain  the  salts  in  solid 
form.  In  other  industries  it  is  often  necessary  to  concentrate  solutions 
by  evaporating  the  larger  part  of  the  liquid  which  they  contain.  The 


FIG.  191. — Diagram  of  a  double  effect  evaporator. 

preparation  of  salt  or  sugar  are  examples  of  such  industries.  In  order 
to  evaporate  the  water  contained,  it  is  usually  necessary  to  heat  the  solu- 
tion to  a  temperature  considerably  higher  than  the  saturation  temperature 
of  the  steam  coming  from  the  solution.  In  order  to  evaporate  a  maximum 
quantity  of  water  by  the  use  of  a  given  quantity  of  heat  (i.e.,  in  order 
to  make  the  evaporator  as  economical  as  possible),  it  is  customary  to  make 
use  of  an  apparatus  usually  termed  a  double-  or  triple-effect  evaporator. 
The  principle  of  operation  of  a  double-effect  evaporator  may  be  seen  by 
reference  to  Fig.  191.  The  evaporation  of  the  liquid  occurs  in  the  pans 
A  and  B.  These  pans  are  provided  with  steam  jackets.  The  jackets 
are  shown  surrounding  the  pans  in  the  illustrations,  although  the  heat 
is  commonly  applied  by  causing  the  steam  to  pass  through  coils  immersed 
in  the  liquid.  Steam  is  supplied  to  the  jacket  of  pan  A  under  high  pres- 
sure, say  100  pounds,  per  square  inch.  The  temperature  of  steam  at  that 
pressure  is  328°  F.  The  steam  which  is  evaporated  from  the  liquid  con- 
tained in  the  pan  is  used  to  jacket  pan  B.  Its  pressure  will  be,  let  us  say, 
20  pounds  per  square  inch  absolute,  which  corresponds  to  a  temperature 

1  So  far  as  it  is  known,  all  air-borne  germs  are  transported  while  adhering  to 
particles  of  floating  dust.  The  elimination  of  dust  from  the  air  supplied  for  venti- 
lation effectually  excludes  such  germs  from  a  room. 


366         HEATING,  VENTILATION,  EVAPORATION,  AND  DRYING     ART.  336 

of  vaporization  228°.  The  difference  in  temperature  of  100°  F.  is  sufficient 
to  evaporate  the  liquid  contained  in  the  pan  A  in  spite  of  the  fact  that  the 
temperature  of  the  liquid  is  considerably  higher  than  the  228°  correspond- 
ing to  the  pressure  of  the  steam  formed.  The  steam  which  is  evaporated 
from  pan  B  is  of  a  pressure,  let  us  say,  of  2  pounds  absolute,  or  at  a  tem- 
perature of  126°.  This  steam  is  condensed  by  the  condenser  C.  A 
vacuum  pump  is  employed  to  remove  the  air  which  is  brought  into  the 
system  by  the  liquid  which  is  to  be  evaporated.  The  condensation  from 
the  jackets  flows  away  through  the  drips  D  and  D'  to  traps  which  permit 
it  to  escape.  It  will  be  seen  that  by  the  employment  of  such  an  apparatus, 
the  heat  which  would  otherwise  be  rejected  with  the  steam  evaporated 
from  the  first  pan  is  utilized  in  evaporating  practically  the  same  weight 
of  liquid  in  the  second  pan.  -This  results  in  doubling  the  efficiency  of 
the  apparatus.  Where  a  high  efficiency  is  desired,  three  or  even  more 
pans  may  be  employed  in  series.  Since  the  temperature  differences 
between  the  steam  in  the  jacket  and  the  liquid  in  the  pan  will  be  reduced 
by  increasing  the  number  of  pans,  it  follows  that  the  first  cost  of  the 
apparatus  required  to  evaporate  a  given  weight  of  liquid  per  hour  will 
increase  as  the  efficiency  is  raised  by  increasing  the  number  of  pans  in 
series.  Evaporators  are  of  many  forms,  and  are  provided  with  numerous 
mechanical  devices,  in  much  the  same  way  as  are  steam  boilers,  in  order 
to  make  their  operation  more  efficient  and  convenient. 

When  exhaust  steam  is  available  it  is  customary  to  employ  it  for  heat- 
ing the  first  pan  in  a  double-effect  evaporator,  making  the  temperature 
drop  per  pan  approximately  50°.  The  capacity  of  the  system  will  be 
quite  largely  increased  by  improving  the  performance  of  the  vacuum 
pumps  and  so  arranging  the  system  that  the  air  to  be  handled  by  the 
pumps  will  be  drawn  from  the  coolest  part  of  the  system  and  will  be  mingled 
with  the  minimum  quantity  of  vapor.  Vacuum  pumps  are  not  needed 
for  those  parts  of  the 'system  where  the  pressure  of  the  steam  is  greater 
than  that  of  the  atmosphere,  since  a  small  portion  of  the  steam  may  be 
permitted  to  escape  through  a  valve,  carrying  the  air  with  it. 

336.  Distilling.  In  some  cases,  it  is  the  vapor  which  is  evaporated 
and  not  the  substance  which  remains  behind  in  the  pan,  which  is  the  valu- 
able product.  In  such  a  case,  the  vapor  must  be  condensed  by  the  use 
of  an  apparatus  termed  a  still.  A  still  consists  of  an  evaporating  chamber 
heated  by  fire  or  by  steam,  and  of  a  coil  of  pipe  usually  termed  a 
worm,  which  is  immersed  in  a  tank  supplied  with  cooling  water  at  the 
bottom,  the  water  being  drawn  away  at  the  top.  Any  form  of  apparatus 
which  will  act  as  a  condenser,  however,  is  equally  suitable  for  use  as  a  still. 
Stills  are  employed  in  the  preparation  of  alcohol,  liquid  ammonia,  kerosene 
and  many  other  volatile  liquids.  When  the  liquids  are  likely  to  bring 
into  a  still  uncondensible  gases,  such  as  air,  it  is  desirable  to  provide 


ART.  337  DRYING  367 

the  still  with  a  vacuum  pump  in  order  that  the  pressure  and  therefore 
the  temperature  of  evaporation  shall  be  as  low  as  possible.  Stills  may 
be  arranged  so  as  to  operate  in  series,  the  vapor  condensed  in  one  worm 
acting  to  evaporate  the  liquid  in  the  second  still. 

337.  Drying.  The  drying  of  substances  containing  only  small  quan- 
tities of  moisture,  as  for  instance,  lumber  cloth,  etc.,  is  usually  effected 
by  exposing  the  substances  to  be  dried  to  a  current  of  dry  air.  At  atmos- 
pheric temperature  air,  of  course,  contains  water  vapor.  Since  the  pressure 
of  the  water  vapor  is  less  than  the  saturation  pressure  corresponding  to  the 
temperature  of  the  air,  the  air  will  absorb  moisture.  It  may  be  caused 
to  absorb  moisture  much  more  rapidly,  however,  by  heating  it,  which 
will  decrease  its  relative  humidity  and  increase  very  greatly  its  capacity 
for  absorbing  moisture  by  raising  the  pressure  of  the  water  vapor  which 
it  can  contain.  If  such  a  current  of  heated  air  be  caused  to  pass  through 
a  pile  of  lumber,  as  is  done  in  the  kiln-drying  process,  it  rapidly  absorbs 
moisture  from  the  lumber  and  passes  out  of  the  kiln  with  a  much  larger 
moisture  content  than  it  had  on  entering.  The  air  is  usually  caused  to 
circulate  by  a  fan  or  other  form  of  mechanical  impeller  and  is  heated 
by  the  use  of  coils  of  steam  pipe.  These  coils  are  usually  supplied  with 
exhaust  steam. 

PROBLEMS 

1.  How  many  cubic  feet  of  air  per  hour  will  be  necessary  to  properly  ventilate 
a  schoolroom  in  which  there  are  thirty  persons?  Ans.     60,000  cu.ft. 

2.  Assuming  that  this  air  is  taken  into  the  building  at  a  temperature  of  32°  F. 
and  a  humidity  of  70  per  cent,  how  many  pounds  of  moisture  will  if  contain? 

Ans.     12.8  Ibs. 

3.  How  many  pounds  of  steam  must  be  introduced  into  this  air  if  the  humidity 
of  the  room  is  to  be  maintained  at  70  per  cent  and  the  temperature  at  68°? 

Ans.     47.6  Ibs. 

4.  A  room  30  ft.  long,  20  ft.  wide,  and  10  ft.  high  is  exposed  at  one  side  and  both 
ends.     It  contains  six  windows  each  3^'X6'.     What  quantity  of  heat  will  be  required 
per  hour  to  provide  against  the  radiation  loss,  if  the  room  is  to  be  maintained  at  a 
temperature  of  68°  F.,    when  the  outdoor  temperature  is  10°  F.,  the  exposure  being 
severe?  Ans.     20,300  B.T.U. 

5.  Assuming  that  four  changes  of  air  per  hour  will  be  required  in  Prob.  4,  what 
total  quantity  of  heat  will  be  required  per  hour?  Ans.     44,700  B.T.U. 

6.  What  quantity  of  direct  steam  radiation  will  be  required  to  heat  the  above 
room?  Ans.     179  sq.ft. 

7.  What  quantity  of  hot-water  radiation  will  be  required  to  heat  the  above  room? 

Ans.     248  sq.ft. 

8.  How  many  cubic  feet  of  air  per  hour  must  be  supplied  by  the  ventilating  system 
to  the  above  room?  Ans.     24,000  cu.ft. 

9.  At  what  temperature  must  the  air  be  introduced  in  order  that  when  it  is  cooled 
down  to  68°,  it  shall  part  with  sufficient  heat  to  provide  against  the  loss  of  heat  by 
radiation?     (Assume  that  the  water  equivalent  of  1  cu.ft.  of  air  is  0.018.)     Ans.   115°. 

10.  How  many  square  feet  of  indirect  radiation  will  be  required  to  warm  this  air 
from  a  temperature  of  10°  F.?  Ans.     117  sq.ft. 


CHAPTER  XXV 
ENTROPY  DIAGRAMS 

338.  Nature  of  the  Temperature-entropy  Diagram.  Entropy  was 
defined  in  Art.  64  as  the  sum  of  the  successive  increments  of  heat  neces- 
sary to  bring  a  body  from  a  fixed  state  to  any  given  state,  each  divided 
by  the  absolute  temperature  at  which  the  increment  of  heat  occurred, 
and  the  definition  expressed  mathematically  by  the  equation 


(1) 


in  which  JN  is  the  change  in  entropy,  JH  is  the  heat  added  (or  abstracted) 
to  produce  this  change  of  entropy,  and  T  is  the  absolute  temperature 
at  which  the  change  occurs.  This  expression  may  be  transformed  into 


(2) 


It  is  very  convenient  and  instructive  in  certain  cases,  to  represent 
thermodynamic  processes  by  plotting  on  a  diagram  the  relation  between 
the  temperature  and  the  entropy  of  the  body  undergoing  the  processes. 
Such  a  diagram  is  called  a  temperature-entropy  diagram.  Its  ordinates 
are  proportional  to  absolute  temperatures,  its  abscissae  to  entropy,  and  its 
areas,  as  may  be  seen  from  equation  (2),  are  proportional  to  heat.  Lines 
on  such  a  diagram  are  termed  temperature-entropy  lines.  Such  a  diagram 
may  be  plotted  for  any  weight  of  substance,  but  it  is  Usual  to  plot  it  for 
1  pound  of  the  substance. 

339.  Forms  of  the  Temperature-entropy  Lines.  Assume  a  body 
whose  mass  is  W,  whose  specific  heat  is  S,  whose  temperature  T0,  and 
whose  entropy  is  zero  (i.e.,  a  body  having  the  zero  state),  to  have  its  tem- 
perature raised  to  the  value  T.  The  head  added  in  order  to  effect  a  given 
small  increase  in  temperature  will  of  course  be 

dH  =  W  S  dT  .........     (1) 

The  corresponding  change  in  entropy  will  be 

,A7       WSdT 
<*N  --      ~T  —  -.       .,,,,,..     (2) 

368 


ART.  339      FORMS  OF  THE   TEMPERATURE-ENTROPY  DIAGRAM          369 
The  entire  change  in  entropy  will  be 

CN  CT dT 

dN  =  WSl     jr -.     .     (3) 

Jo  JT,    1 

Integrating,  we  will  have 

T 

- (4) 


Plotting  this  relation  on  a  temperature-entropy  diagram,  we  will  have  the 
temperature-entropy  line  shown  in  Fig.  192.  As  may  be  seen  from  this 
figure,  the  entropy  of  the  body  at  the  zero  state  (i.e.,  the  temperature  T0) 
is  zero,  the  entropy  of  the  body  at  temperature  T  is  N}  and  the  quan- 


dN 


o      d 

FIG.  192. 


FIG.  193. 


tity  of  heat  required  to  raise  the  temperature  from  T0  to  Tb  will  be  repre- 
sented by  the  areas  a-b-d-o,  as  will  appear  from  the  following  : 

The  strip  on  the  diagram  whose  width  is  dN  and  whose  height  is  T 
has  the  area  T  dN  =dH  in  which  dH  is  the  quantity  of  heat  imparted 
in  order  to  change  the  entropy  by  the  quantity  dN.  The  total  quantity 
of  heat  imparted  in  changing  the  body  from  the  zero  state  to  state  B  is 
the  sum  of  all  such  strips  included  under  the  line  a-b.  Hence,  the  heat 
imparted  is  equal  to  the  area  included  under  the  line. 

When  a  body  is  heated  without  raising  its  temperature,  as,  for  instance, 
when  water  is  evaporated  into  steam,  or  a  quantity  of  gas  expands  adi- 
abatically,  the  increase  of  entropy  occurs  at  constant  temperature  and  the 
temperature-entropy  line  is  horizontal,  as,  for  instance,  the  line  a-b  in 
Fig.  193.  When  a  body  changes  in  temperature  without  receiving  or 


370 


ENTROPY  ^DIAGRAMS 


ART.  340 


emitting  heat,  as  for  instance,  when  a  quantity  of  gas  or  vapor  expands 
adiabatically,  the  entropy  is  unchanged  and  the  temperature-entropy  line 
is  vertical,  as  is  the  line  b-c  in  .Fig.  193.  When  a  body  absorbs  or  emits 
heat  and  simultaneously  changes  in  temperature,  and  the  quantity  of  heat 
absorbed  or  emitted  is  proportional  to  the  changes  in  temperature, 
the  temperature-entropy  line  will  be  of  the  form  represented  by  the 
equation 

.........     (5) 


Such  will  be  the  case  when  the  specific  heat  of  the  body  is  constant,  or 
when  a  gas  is  heated  at  constant  pressure  or  constant  volume  or  under- 
goes poly  tropic  expansion.  When  K  is  positive  (i.e.,  when  conditions 


o  f 


FIG.  194. 


FIG.  195. 


are  such  that  the  body  rises  in  temperature  as  heat  is  added,  or  falls 
in  temperature  as  heat  is  abstracted,  the  general  direction  of  the  tem- 
perature-entropy line  will  be  like  that  of  a-b  in  Fig.  194.  When  K  is 
negative  (i.e.,  when  a  fall  in  temperature  accompanies  an  absorption  of 
heat  or  a  rise  in  temperature  and  emission  of  heat)  the  general  direction 
is  that  of  line  c  d  in  the  same  figure. 

340.  Thermodynamic  Cycles  on  the  Temperature-entropy  Plane. 
Any  thermodynamic  process  involving  a  body  of  constant  mass  may  be 
represented  by  an  appropriate  temperature-entropy  line.  Any  series 
of  such  processes  may  be  represented  by  a  series  of  temperature-entropy 
lines,  just  as  they  may  be  represented  by  a  series  of  pressure  volume  lines. 
Such  a  diagram  may  be  drawn  to  represent  any  thermodynamic  cycle, 
and  the  cycle  is  then  said  to  be  represented  on  the  temperature-entropy 
plane.  The  diagram  in  Fig.  195  represents  the  Carnot  cycle  in  which 
the  working  fluid  expands  isothermally  from  state  a  to  state  b  at  the 


ART.  341 


EVAPORATION  AND  SUPERHEATING 


371 


temperature  Tlt  receiving  from  the  heater  the  quantity  of  heat  represented 
by  the  area  a-b-e-f.  The  line  b-c  represents  the  process  of  adiabatic 
expansion.  The  line  c-d  represents  the  process  of  isothermal  compression 
at  the  temperature  T2,  the  quantity  of  heat  represented  by  the  area 
c-d-f-e  being  rejected  to  the  cooler  during  this  process.  The  line  d-a 
represents  the  process  of  adiabatic  compression.  An  inspection  of  this 
diagram  will  serve  to  show  that  the  heat  absorbed  is  to  the  heat  rejected 
as  the  temperature  Tl  is  to  the  temperature  T2.  Consequently,  it  may 
be  shown  from  the  diagram  that  the  efficiency  of  the  Carnot  cycle,  which  is 


is  also  equal  to 


HI 

T.-T2 


Any  other  cycle  in  which  a  constant  mass  of  working  fluid  is  employed 
or  which  is  the  equivalent  of  a  cycle  in  which  a  constant  mass  of  working 
fluid  is  employed,  may  be  represented  by  the  temperature-entropy 
diagram.  In  case,  however,  a  variable  quantity  of  working  fluid  is 
employed,  as  is  the  case  in  the  practical  steam-engine  cycle,  only  those 
processes  can  be  properly  represented  on  a  temper- 
ature-entropy  diagram  during  which  the  quantity 
of  working  fluid  remains  constant. 

341.  Evaporation  and  Superheating  on  the 
Temperature-entropy  Plane.  The  process  of  rais- 
ing a  quantity  of  water  from  the  zero  state  (i.e., 
from  the  liquid  state  at  a  temperature  of  32  °F)  to 
any  temperature  T,  evaporating  it  into  steam,  and 
then  superheating  the  steam  at  constant  pressure, 
is  represented  on  the  temperature-entropy  diagram 
by  three  lines  of  the  form  shown  in  Fig.  196.  Line 
a—b  represents  the  process  of  raising  the  tempera- 
ture of  the  liquid  from  32°  to  T.  Since  the 
specific  heat  of  water  is  very  nearly  but  not 
exactly  a  constant  quantity,  this  line  may  be 
represented  very  nearly,  but  not  exactly  by  the  equation 


t 


I 

I 


o    s 


FIG.  196. 


T 

To 


(1) 


During  the  evaporation  of  the  water  the  temperature  of  the  entire  mass 
remains  constant  and  the  entropy  increases.  The  process  is  the  equivalent 
of  isothermal  expansion,  and  is  represented  by  the  line  b-d.  The  process 
of  superheating  the  steam  is  represented  by  the  line  c-d,  which  has  approx- 


372 


ENTROPY  DIAGRAMS 


ART.  342 


imately  the  logarithmic  form  already  given,  although  it  does  not  approx- 
imate this  form  as  nearly  as  does  the  line  a-b,  since  the  specific  heat  of 
steam  at  most  pressures  varies  a  little  with  the  temperature.  On  this 
diagram,  the  area  a-b-g—o  represents  the  heat  of  the  liquid,  the  area  b—c- 
f-g  represents  the  heat  of  evaporation,  and  the  area  c-d-e-f  represents 
the  heat  of  superheat. 

342.  The  Steam  Dome.  Fig.  197  represents  a  form  of  temperature 
diagram  often  termed  the  steam  dome.  The  line  a-b  represents  the  rela- 
tion between  the  temperature  and  entropy  of  water,  and  is  termed  the 


r  m  i  p 


FIG.  197. 

water  line.  The  line  c—d  represents  the  relation  between  the  temperature 
and  entropy  1  of  dry  and  saturated  steam,  and  is  termed  the  saturation 
line.  Horizontal  lines  between  ab,  and  cd,  like  b-c,  e-f,  g-h,  etc.,  represent 
the  relation  between  the  temperature  and  entropy  of  wet  steam  of  a 
given  constant  temperature,  but  of  varying  quality.  The  lengths  of  any 
of  these  lines,  in  entropy  units,  is,  of  course,  the  entropy  of  evaporation 
of  dry  and  saturated  steam  of  the  given  temperature.  Since  the  quality 
of  steam  of  a  given  pressure  is  proportional  to  its  latent  heat  of  evapora- 
tion, which  in  turn  is  proportional  to  its  heat  of  evaporation,  which  in 
turn  is  proportional  to  its  entropy  of  evaporation,  any  temperature- 
entropy  line  drawn  in  such  a  way  as  to  divide  these  horizontal  lines  into 

1  When  the  entropy  as  steam  is  mentioned  in  this  chapter,  the  total  entropy  is  meant. 


ART.  343     TEMPERATURE-ENTROPY  DIAGRAM  FOR  STEAM  CYCLES     373 

segments  bearing  a  constant  ratio  to  one  another,  is  a  line  of  constant 
quality,  and  represents  the  relation  between  the  temperature  and  entropy 
of  steam  of  a  given  quality.  Line  i-k  is  such  a  line,  and  the  ratio  of  any 
segment,  as  bi,  to  the  whole  line,  as  be,  gives  the  quality  of  the  steam. 
Vertical  lines  on  the  steam  dome  are,  of  course,  lines  of  constant  entropy. 
Lines  of  the  form  l-m  and  n-o  are  lines  of  constant  volume  and  represent 
the  relation  between  the  temperature  and  entropy  of  a  given  volume  of 
wet  steam  at  different  pressures.  Lines  of  the  form  p-q  and  r-s  are  lines 
of  constant  total  heat,  and  represents  the  relation  between  the  temperature 
and  entropy  of  wet  steam  of  varying  pressure  but  of  a  given  total  heat. 
In  order  to  save  space,  it  is  customary  to  cut  off  that  part  of  this  diagram 
which  lies  below  the  temperature  of  32°  F.,  (i.  e.  the  point  a)  unless  it 
is  necessary  to  use  it  for  some  reason. 

An  inspection  of  this  diagram  will  serve  to  make  clear  a  great  many 
points  in  regard  to  the  properties  of  steam.  It  will  be  seen,  for  instance, 
that  dry  steam  expanding  adiabatically  becomes  wet.  On  the  other 
hand,  steam  having  a  quality  of  less  than  about  50  per  cent  becomes  dryer 
as  a  result  of  adiabatic  expansion.  It  will  be  seen  that  when  steam 
expands  without  alteration  in  its  total  heat,  as  it  does  when  throttled, 
the  steam  becomes  dryer.  Were  the  lines  a-b  and  c-d  continued  upward 
sufficiently,  they  would  finally  meet  at  the  critical  temperature  of  the 
vapor. 

343.  Temperature-Entropy  Diagram  for  Steam  Cycles.  The  tem- 
perature-entropy diagram  of  the  Camot  cycle  for  steam  is  exact!}- 
the  same  as  it  would  be  for  any  working  fluid  absorbing  the  same 
quantity  of  heat  and  working  through  the  same  temperature  range. 
In  Fig.  198  will  be  found  the  temperature-entropy  diagrams  of  Carnot 
cycles  for  steam  superimposed  upon  the  steam  dome,  for  different  con- 
ditions, each  diagram  being  accompanied  by  the  corresponding  pressure 
volume  diagram. 

The  temperature-entropy  diagram  of  the  Rankine  cycle  for  dry 
steam  is  illustrated  in  Fig.  199.  Line  b-c  represents  the  isothermal 
expansion  of  the  steam  as  it  enters  the  cylinder,  line  c-d  represents  adi- 
abatic expansion,  line  d-e  represents  the  isothermal  compression  and  con- 
densation, and  line  e-b  represents  the  heating  of  the  condensing  steam  to 
its  initial  temperature.  The  work  done  is,  of  course,  represented  by  the 
area  b-c-d-e.  The  heat  imparted  is  represented  by  the  area  b-c-f-g-e. 
An  inspection  of  the  diagram  will  show  that  the  efficiency  of  the  Rankine 
cycle  must  be  less  than  that  of  the  Carnot  cycle.  That  portion  of  the 
heat  supplied  which  is  represented  by  the  area  e-b-h-g,  performs 
work  represented  by  the  area  e-b-4f  and  the  efficiency  of  this  portion  of 

the  heat  supply  is  -  This  is  manifestly  less  than  the  efficiency  of  the 

ebhg 


374 


ENTROPY   DIAGRAMS 


ART.  343 


Carnot  cycle  working  through  the  same  temperature  range,  which  is 

jbie 
jbhg' 

The  temperature-entropy  diagram  of  the  Rankine  cycle,  using  wet 
steam,  is  shown  in  Fig.  200.  It  will  be  seen  from  this  figure  that  the  pro- 
portion of  the  total  heat  used  inefficiently  becomes  greater  as  the  quality 


FIG.  198. 

of  the  steam  becomes  less.  Hence  the  efficiency  of  the  cycle  is  less  when 
wet  steam  is  used.  The  diagram  of  the  Rankine  cycle  using  superheated 
steam  is  shown  in  Fig.  20 1,  from  which  it  may  be  seen  that  the  superheated 
steam  is  more  efficient  than  saturated  steam  of  the  same  pressure,  but  not 
as  efficient  as  saturated  steam  of  the  same  temperature.  It  will  be  noted 
that,  as  the  steam  expands,  its  superheat  decreases  and  finally  at  the 
point  i,  the  adiabatic  crosses  the  saturation  line  and  the  steam  becomes 
wet. 


ART.  343    TEMPERATURE-ENTROPY  DIAGRAM  FOR  STEAM  CYCLES    375 


A  temperature-entropy  diagram  of  the  modified  Rankine  cycle  may  be 
seen  in  Fig.  202.     The  cylinder  contains  a  pound  of  working  fluid,  a  portion 


J* 


d\ 


O      g    h  I 

FIG.  199. 


/ 

b                              c 

/ 

—  \ 

\ 
a 

\ 

\ 

e 

OS  f 

FIG.  200. 


l\ 


FIG.  201. 


FIG.  202. 


\ 
\ 
\ 
\ 
\ 
d     \ 


\ 


of  which  remains  in  the  clearance  space  and  is  adiabatically  compressed, 
while  the  remainder  passes  to  the  boiler  where  its  temperature  is  raised 
while  it  is  in  the  liquid  state,  by  the  application  of  heat.  In  order  to 


376 


ENTROPY   DIAGRAMS 


ART.  343 


draw  the  temperature-entropy  diagram  of  this  cycle,  it  is  necessary  to 
assume  that  the  water  in  the  boiler  has  the  same  temperature  at  every 
instant  during  the  compression  period  as  does  the  cushion  steam.  The 
cushion  steam  is  of  course  compressed  adiabatically,  but  the  compression 
line  e-b  is  not  an  adiabatic,  since  it  represents  the  relation  between  the 
temperature  and  entropy  of  the  whole  quantity  of  working  fluid  and  not 
simply  that  of  the  cushion  steam.  In  this  diagram,  line  a-h  is  the  water 
line  for  1  pound  of  working  fluid  and  line  a  i  is  the  water  line  for  that 
weight  of  working  fluid  rejected  from  the  cylinder  each  cycle.  The 
abscissa  /  represents  the  entropy  of  the  liquid  rejected  from  the  cycle 
at  some  temperature,  the  abscissa  k  represents  the  entropy  of  1  pound 
of  water  at  the  same  temperature,  the  abscissa  /  represents  the  total 


o   ts 


h  \ 
\ 

\ 
\ 

a     \ 


FIG.  203. 


FIG.  204. 


entropy  of  the  working  fluid  during  the  compression  period,  at  that  tem- 
perature, and  the  distance  m  (which  is  equal  to  I  —f)  represents  the  total 
entropy  of  the  cushion  steam  at  that  temperature.  Since  the  cushion 
steam  is  compressed  adiabatically,  its  entropy  remains  constant  during 
the  compression  period,  and  the  distance  m  also  remains  constant. 

The  temperature-entropy  diagram  of  the  jacketed  cycle  with  com- 
plete expansion  is  shown  in  Fig.  203.  The  heat  added  is  now  represented 
by  the  area  e—b—c—d—f-g}  while  the  work  performed  is  represented  by  the 
area  e-b-c-d.  The  heat  added  by  the  jacket  is  represented  by  the  area 
c-d-f-h,  and  the  work  done  by  this  heat  by  the  area  c-d-4.  It  will  be 
apparent  that  the  heat  supplied  by  the  jacket  is  used  less  efficiently 
than  that  supplied  by  the  cylinder  feed,  and  that  the  efficiency  of  the 
jacketed  cycle  is  theoretically  less  than  that  of  the  un jacketed  cycle. 


ART.  343     TEMPERATURE-ENTROPY  DIAGRAM  FOR  STEAM  CYCLES     377 


The  temperature-entropy  diagram  of  the  imperfect  cycle  without 
clearance  and  using  dry  steam  is  shown  in  Fig.  204.  That  portion  of 
the  cycle  lying  within  the  area  i  h  d,  and  cut  off  from  the  remainder  of 
the  diagram  by  the  constant  volume  line  i—h,  is  work  lost  on  account 
of  incomplete  expansion.  The  less  complete  the  expansion,  the  greater 
will  be  the  quantity  of  work  so  lost,  the  constant-volume  line  c-j  represent- 
ing the  limiting  condition  in  which  there  is  no  expansion  and  the  indicator 
card  given  by  the  engine  is  rectangular.  The  temperature-entropy  dia- 
gram of  the  jacketed  cycle  with  incomplete  expansion  is  shown  in  Fig. 
205,  from  which  it  may  be  seen  that  in  case  the  expansion  is  incomplete, 


o    g 


\ 


h  I 


FIG.  205. 


FIG.  206. 


the  efficiency  of  the  heat  supplied  by  the  jacket  is  even  less  than  when 
the  expansion  is  complete. 

In  drawing  the  temperature-entropy  diagram  of  the  imperfect  cycle 
with  clearance,  it  is  necessary  to  assume,  as  we  did  in  the  case  of  the 
Rankine  cycle  with  complete  compression,  that  the  water  in  the  boiler 
has  the  same  temperature  as  the  cushion  steam  at  every  instant  during 
the  compression  period  and  that  the  sum  of  the  weights  of  the  cushion 
steam  and  the  water  in  the  boiler  is  1  pound.  By  employing  such 
assumptions  the  temperature-entropy  diagram  may  be  drawn,  but  this 
temperature-entropy  diagram  will  not,  of  course,  represent  truly  the  actual 
condition  of  affairs  in  a  real  engine. 

In  Fig.  206  may  be  seen  the  temperature-entropy  diagram  of  the 
imperfect  cycle  with  complete  compression.  The  line  e-b  is  the  com- 
pression line  and  is  found  in  a  manner  similar  to  the  line  e-b  in  Fig.  202. 


378 


ENTROPY   DIAGRAMS 


ART.  343 


The  work  lost  on  account  of  clearance  is,  of  course,  the  area  f  be  e' .  How- 
ever, on  account  of  the  cushion  steam  contained  in  the  clearance  spaces 
it  is  unnecessary  to  add  the  heat  represented  by  the  area  g'  e'  f  b  e  g.  The 
ratio  of  the  work  lost  to  the  heat  saved  is,  however,  greater  than  the  ratio 
of  the  work  done  (area  e  b  c  h  i)  to  the  heat  actually  added  (area  g  e  b  c  f) 
and  on  this  account  the  efficiency  of  the  cycle  is  reduced  by  the  use  of 
clearance. 

In  Fig.  207  will  be  seen  the  temperature-entropy  diagram  of  an 
imperfect  cycle  having  clearance  and  no  compression.  The  line  e-b 
represents  the  rise  in  pressure  due  to  the  introduction  of  steam  from  the 
boiler,  and  is  a  constant  volume  line.  It  will  be  seen  that  the  ratio  of  the 


o    g'g 


FIG.  207. 


O       g  g' 


FIG.  208. 


work  lost  on  account  of  clearance,  (area  /  b  e  e')  to  the  heat  saved, 
(area  g'  e'  j  b  e  g)  is  much  greater  than  the  ratio  of  the  work  lost  to  the  heat 
saved  in  Fig.  206.  The  use  of  compression  therefore  raises  the  efficiency 
of  the  cycle. 

In  Fig.  208  will  be  seen  the  temperature-entropy  diagram  of  the 
imperfect  cycle  writh  partial  compression.  The  compression  line  is  line 
e-kj  the  admission  line  is  line  k-b,  the  steam  line  is  line  b-c,  the  expansion 
line  is  line  c-k,  the  release  line  is  line  h-^i,  and  the  exhaust  line  is  line 
i-e.  The  heat  supplied  is  represented  by  the  area  g  e  k  b  c  f,  while  the  work 
done  is  represented  by  the  area  e  b  c  h  i.  The  area  i  h  d  represents  the 
loss  due  to  incomplete  expansion.  The  area  k  m  b  represents  the  loss  due 
to  incomplete  compression.  This  loss,  however,  cannot  be  diminished  by 


ART.  344  DIAGRAM  FOR  THE  ACTUAL  STEAM   ENGINE 


379 


increasing  the  compression  pressure,  since,  with  the  clearance  volume  shown 
by  the  diagram,  if  the  compression  pressure  be  raised  until  the  compres- 
sion is  complete,  the  lost  work  due  to  clearance  wiU  be  increased  by  the 
area  e'  e  k  b,  while  the  heat  saved  will  be  represented  by  the  area  g  e  k  b  e' 
gf.  If  the  ratio  of  the  work  lost  to  the  heat  saved  is  greater  than  the  ratio 
of  the  work  done  to  the  heat  supplied  for  the  whole  cycle,  compression 
has  been  carried  to  too  high  a  point. 

344.  The  Temperature-Entropy  Diagram  for  the  Actual  Steam  Engine. 
In  Fig.  209  will  be  found  such  a  temperature-entropy  diagram  as  would 
actually  be  obtained  from 
a  steam  engine.  The  line 
a-b  represents  the  period 
of  admission.  It  will  be 
seen  that  the  temperature 
falls  during  this  period  on 
account  of  the  fall  in  pres- 
sure due  to  wire  drawing, 
and  that  throughout  the 
admission  period  the  steam 
line  remains  below  the 
evaporation  line  g-h,  which 
represents  the  temperature 
of  the  steam  in  the  boiler. 
It  is  assumed  that  the  steam 
is  slightly  wet  as  it  enters 
the  cylinder,  so  that  the 
point  h,  which  is  the  state 
point  of  the  steam  coming 
from  the  boiler,  does  not 
fall  on  the  saturation  line. 
The  line  b-c  represents 
the  expansion  period .  If  the 
expansion  were  adiabatic, 
the  line  would  be  vertical. 
Actually  the  line  is  of  the  pIG  209. 

curved    form    shown.      At 

the  point  where  the  admission  ceases  it  will  be  noted  that  the  line  begins 
to  run  to  the  left,  indicating  that  the  steam  is  parting  with  heat  more 
rapidly  than  it  would  as  a  result  of  adiabatic  expansion.  This  is  because 
cylinder  condensation  has  not  ceased  at  cut  off,  but  continues  until 
the  temperature  of  the  steam  is  below  the  average  temperature  of  the 
surface  of  cylinder  walls.  At  the  point  where  the  tangent  to  the  expansion 
line  is  vertical,  the  rate  of  evaporation  of  steam  from  the  clearance  area 


380  ENTROPY   DIAGRAMS  ART.  345 

is  equal  to  the  rate  of  Condensation  upon  that  portion  of  the  barrel  which 
is  just  being  uncovered  by  the  moving  piston,  and  from  that  point  onward 
re-evaporation  is  more  rapid  than  condensation.  As  a  result,  the  line 
tends  toward  the  right,  indicating  an  addition  of  heat.  At  c,  release 
occurs.  The  line  c-d  is  not,  however,  a  line  of  constant  volume,  since 
release  does  not  occur  at  the  end  of  the  stroke,  and  the  fall  in  pressure 
is  gradual  and  not  sudden  on  account  of  wire  drawing  through  the  exhaust 
ports.  The  line  d-e  represents  the  period  of  exhaust  during  which  the 
back  pressure  remains  practically  constant.  The  line  e-f  represents  the 
period  of  compression  during  which  the  pressure  and  temperature  of 
the  steam  rises.  The  pressure  and  temperature  of  the  cylinder  feed  in  the 
boiler  is  assumed  to  rise  simultaneously.  As  has  been  previously  noted, 
the  line  d-f  will  not  be  a  vertical  line,  in  spite  of  the  fact  that  the  com- 
pression of  the  cushion  steam  is  adiabatic,  since  that  portion  of  the  work- 
ing fluid  which  is  contained  in  the  boiler  is  receiving  additions  of  heat 
during  the  compression  period.  The  line  f-a  is  the  admission  line,  and 
is  of  course,  a  constant  volume  line. 

345.  Graphical  Analysis  of  the  Losses  in  a  Steam  Engine.  The  actual 
temperature-entropy  diagram  for  a  steam  engine  may  be  superimposed 
upon  the  Rankine  cycle  temperature-entropy  diagram  in  order  to  deter- 
mine the  amount  and  distribution  of  losses  in  the  engine.  In  Fig.  209 
I  p  h  q  is  the  Rankine  cycle  diagram  with  complete  compression  for  1 
pound  of  working  fluid  between  the  temperature  limits  of  the  boiler  and  the 
discharged  condensing  water.  The  quantity  of  heat  supplied  is  n  I  p  h  m. 
Of  this  heat,  the  quantity  n  I  q  m  would  be  lost  in  the  exhaust  of  the 
Rankine  cycle,  while  the  remainder  would  be  transformed  into  work. 
Since  the  imperfect  cycle  is  employed,  that  quantity  of  work  represented 
by  the  area  k  i  q  is  lost  on  account  of  incomplete  expansion  and  that  quan- 
tity represented  by  /  p  a'  is  lost  on  account  of  incomplete  compression. 
It  is  unnecessary,  however,  to  supply  the  quantity  of  heat  represented 
by  this  small  area,  but  since  this  entire  quantity  of  heat  would  be  trans- 
formed into  work,  a  considerable  loss  is  represented  by  its  absence.  The 
area  e'  d'  k  I  represents  the  loss  due  to  imperfect  condenser  action.  The 
area  bf  h  i  cf  represents  the  power  loss  with  the  given  quantity  of  steam 
and  the  given  terminal  volume  due  to  cylinder  condensation.  The  area 
d'  c'  j  then  represents  the  theoretical  loss  resulting  from  the  fact  that  the 
actual  expansion  line  is  not  continued  to  the  back  pressure  line,  following 
the  same  law  of  expansion  as  it  does  from  &'  to  c' ' .  Were  the  expansion 
continued  to  this  point,  however,  as  a  result  of  the  increased  temperature 
range  of  the  cylinder  walls,  the  form  of  the  temperature-entropy  diagram 
would  be  changed,  and  the  distribution  of  losses  altered  considerably. 
The  shaded  areas  represent  the  loss  which  results  from  wire  drawing  and 
fluid  friction  and  the  ratio  of  the  actual  temperature-entropy  diagram 


ART.  346  DIAGRAM   FOR  COMPOUND   ENGINE  381 

to    the   diagram    bounded  by   a'  bf  c'  d'  e'  /  is  the  card   factor  of  the 
engine. 

It  must  not  be  inferred  that  all  heat  losses  shown  by  the  temperature- 
entropy  diagram  are  due  to  the  direct  transfer  of  heat  to  or  from  the  steam. 
They  may  be  due  to  the  loss  of  steam  from  the  working  chamber  on  account 
of  leakage.  On  the  temperature-entropy  diagram,  as  on  the  indicator 
card,  leakage  shows  exactly  the  same  effects  as  does  cylinder  condensa- 
tion. We  cannot  therefore  infer  that  the  heat  transfer  shown  occurs 
between  working  fluid  and  the  cylinder  wall. 

346.  Temperature-Entropy  Diagram  for  Compound  Engine.     Usually 
the  weight  of  the  working  fluid  contained  at  cut-off  in  the  high-pressure 
cylinder  of  a  compound  engine  is  different  from  that  contained  at  cut-off 
in  the  low-pressure  cylinder  on  account  of  the  difference  in  the  weight  of 
the   cushion  steam.     It  is  therefore  impossible  to  draw  a  temperature- 
entropy  diagram  which  represents  the  behavior  of  the  steam  in  such  an 
engine,  although  such  a  diagram  may  be  drawn  for  each  cylinder  separately. 
The  diagram  of  the  low-pressure  cylinder  will  fall  below  that  of  the  high- 
pressure  cylinder  when  they  are  superimposed  on  the  same  steam  dome, 
and  they  may  slightly  overlap  in  case  the  indicator  cards  overlap.     Since 
a  temperature-entropy  diagram  is  always  drawn  for  1  pound  of  working 
fluid,  it  follows  that  the  weight  of  the  cylinder  feed  shown  by  the  two 
diagrams  will  be  different,  and  it  is  necessary,  therefore,  to  treat  the  losses 
occurring  in  each  cylinder  separately.     The  quantity  of  heat  supplied  to 
the  second  cylinder  per  pound  of  cylinder  feed  will  be  equal  to  the  total 
quantity  of  heat  rejected  from  the  first  cylinder  per  pound  of  cylinder  feed, 
less  the  quantity  of  heat  lost  from  the  first  cylinder  by  radiation,  which  is 
usually  extremely  small.     Hence,  in  order  to  obtain  the  efficiency  of  a 
compound  engine  from  such  a  combined  temperature-entropy  diagram, 
it  is  necessaiy  to  obtain  the  efficiency  shown  by  each  diagram  separately, 
in  which  case  the  efficiency  of  the  engine  will  be  the  efficiency  shown  by 
the  high-pressure  diagram  plus  the  efficiency  shown  by  the  low-pressure 
diagram,  multiplied  by  one  minus  the  efficiency  shown  by  the  high-pres- 
sure diagram.     The  temperature-entropy  diagram  for  a  compound  engine 
may  be  employed  in  order  to  analyze  the  heat  transfers  occurring  within 
each  of  its  cylinders,  and  will  show  the  causes  and  relative  amounts  of  the 
losses  in  each  of  the  cylinders. 

347.  Transferring  an  Indicator  Diagram  to  the  Temperature-Entropy 
Plane.     In  order  to  employ  the  temperature-entropy  diagram  to  illus- 
trate graphically  the  distribution  of  losses  in  the  steam  engine,  it  is  neces- 
sary to  have  an  indicator  card  representative  of  the  average  conditions 
in  the  two  ends  of  the  cylinder  of  the  engine  for  the  entire  test,  and  to 
transfer  it  to  the  temperature-entropy  plane.     In  Fig.  210  such  a  card  is 
shown,  in  the  quadrant  P  0  V.     In  the  quadrant  P  0  T  is  the  pressure- 


382 


ENTROPY   DIAGRAMS 


ART.  347 


temperature  curve  of  saturated  steam.  In  the  quadrant  T  0  N,  which 
is  the  temperature-entropy  plane,  the  desired  temperature-entropy  dia- 
gram is  to  be  drawn.  In  the  quadrant  V  0  N  is  drawn  the  line  H  H,  which 
gives  the  relation  between  the  volume  and  the  entropy  of  1  pound  of 
water.  Since  the  distance  of  line  H  H  from  line  0  N  is  extremely  small 
as  compared  with  the  other  distances  to  be  measured  in  this  quadrant, 
no  serious  error  will  be  introduced  if  this  line  is  omitted  and  the  con- 
structions are  based  upon  line  0  N  instead  of  line  H  H.  The  saturation 
curve  for  the  quantity  of  steam  which  the  test  shows  to  be  contained  in  the 
cylinder  per  revolution  at  cut-off,  is  next  drawn  in  the  quadrant  P  0  V, 
and  is  the  line  R  Q.  In  the  quadrant  TON  are  drawn  the  lines  0  W  and 

S  N,  the  first  being 
the  water  line  and 
the  second  the  satu- 
ration line.  In  order 
to  transfer  any  point 
on  the  indicator  card, 
as,  for  instance,  point 
B,  to  the  temperature- 
entropy  plane,  the 
following  construction 
is  employed.  Draw 
line  A  C  through  B, 
then  draw  lines  A  D 
and  C  E.  Next  draw 
lines  E  D  and  G  H, 
then  D  H,  then  B  F, 
and  finally  F  I.  The 
intersection  of  C  E 
and  S  N  determines 

the  entropy  of  1  pound  of  dry  and  saturated  steam  at  the  temperature 
represented  by  point  B.  The  entropy  of  evaporation  of  the  wet  steam  at 
point  B  is  proportional  to  the  increase  in  its  volume  which  results  from 
its  evaporation  (i.e.,  to  its  quality).  By  the  construction,  we  have 
divided  the  evaporation  line  G  E  into  two  segments,  one  of  which,  G  I 
bears  the  same  ratio  to  G  E,  as  the  volume  of  the  steam  at  B  does  to  the 
specific  volume  of  dry  and  saturated  steam.  The  point  /  is  therefore  the 
state  point  on  the  temperature-entropy  diagram  of  the  point  B  on  the 
pressure-volume  diagram.  Other  points  on  the  temperature-entropy 
diagram  may  be  found  in  the  same  way,  and  the  diagram  drawn. 

348.  The  Temperature-Entropy  Diagram  for  the  Steam  Turbine. 
Since  a  single-stage  steam  turbine  operates  upon  the  Rankine  cycle,  the 
theoretical  temperature-entropy  diagram  will  be  that  of  the  Rankine  cycle 


FIG.  210. 


ART.  348 


DIAGRAM  FOR  THE   STEAM  TURBINE 


383 


for  steam  of  the  quality  supplied  to  the  turbine.  Turbines  are  usually 
supplied  with  superheated  steam  so  that  the  temperature-entropy  diagram 
will  usually  have  the  form  shown  in  Fig.  201.  However,  after  the  steam 
has  passed  through  the  nozzle  of  the  turbine,  it  loses  a  portion  of  its 
kinetic  energy,  which  is  retransformed  into  heat  by  eddying  and  fluid 
friction,  so  that  although  the  kinetic  energy  of  the  steam  flowing  from  a 
nozzle  is  in  theory  equal  to  the  area  e  b  c  h  d,  the  work  which  actually 
is  transferred  to  the  rotating  member  is  much  less. 

Actually,  the  expansion  of  the  steam  in  the  turbine  nozzle  is  not 
quite  adiabatic,  since  on  account  of  friction,  its  entropy  is  continually 
increased  by  the  retransformation  of  a  portion  of  its  kinetic  energy  into 


I 


i  k 


FIG.  211. 


FIG.  212. 


heat.  The  diagram  which  represents  the  condition  of  affairs  in  such  a 
nozzle  is  shown  in  Fig.  211,  in  which  line  c  d  represents  the  relation  between 
the  temperature  and  the  entropy  of  the  expanding  steam.  The  kinetic 
energy  of  the  jet  proceeding  from  the  nozzle  is  not,  however,  equal  to 
the  area  b  c  d  e,  since  a  portion  of  the  work  generated  was  transformed 
into  the  heat  represented  by  the  area  c  d  g  f.  The  actual  kinetic  energy 
of  the  issuing  jet  is  equal  to  the  area  b  c  d  e  minus  the  area  i  d  f  g. 
The  amount  of  heat  represented  by  the  area  i  d  f  g  is  exceedingly 
small,  however,  when  the  nozzle  is  properly  designed,  and  its  effect  in 
modifying  the  temperature-entropy  diagram  is  almost  imperceptible. 
The  heat  supplied  in  the  entering  steam  is,  of  course,  represented  by  the 
area  h  e  b  c  g. 


384 


ENTROPY    DIAGRAMS 


ABT.  349 


In  Fig.  212  may  be  seen  the  temperature-entropy  diagram  of  a  two- 
stage  impulse  turbine.  A  part  of  the  kinetic  energy  of  the  jet  issuing 
form  the  nozzles  in  the  first  stage  is  retransformed  into  the  quantity  of 
heat  represented  by  the  area  f  k  I  d.  The  equivalent  area  is  shown  sub- 
tracted from  the  work  of  the  first  stage  and  is  represented  by  the  shaded 
area  within  e  b  c  d.  In  like  manner,  in  the  second  stage,  a  portion  of  the 
work  efghis  retransformed  into  the  quantity  of  heat  represented  by  the 
area  g  i  j  k  and  is  shown  by  the  shaded  area  taken  out  of  e  fg  h.  The  heat 

supplied  in  the  entering  steam  is 
represented  by  the  area  m  h  b  c  I, 
and  the  useful  work  is  measured  b> 
the  unshaded  area  included  within 
h  b  c  d  f  g. 

In  the  case  of  a  turbine  contain- 
ing a  very  large  number  of  stages, 
^  whether  it  be  an  impulse  turbine  or 
\  an  impulse  reaction  turbine,  the  tem- 
perature-entropy diagram  will  have 
approximately  the  form  shown  in 
Fig.  213.  The  quantity  of  heat 
added  is  that  represented  by  the  area 
h  e  b  c  g.  A  portion  of  the  kinetic 
energy  of  the  steam  flowing  in  the 
vanes  is  retransformed  into  the  quan- 
tity of  heat  represented  by  the  area 
c  d  f  g  and  the  relation  between  the 
temperature  and  entropy  of  the  steam 
as  it  traverses  the  turbine  is  repre- 
sented by  the  line  c  d.  The  total 

amount  of  heat  transformed  into  work  is  represented  by  the  area  e  b  c  d 
minus  the  area  i  d  f  g. 

349.  The  Total  Heat-Entropy  or  Mollier  Diagram.  It  is  very  convenient 
in  designing  thermodynamic  apparatus,  particularly  in  the  case  of  steam 
turbines,  to  make  use  of  the  Mollier  diagram,  which  gives  graphically  the 
relation  between  the  total  heat  and  total  entropy  of  steam.  Such  a 
diagram  accompanies  both  Marks  and  Davis'  and  Peabody's  steam  tables, 
and  is  shown  in  skeleton  in  Fig.  214.  On  this  diagram  are  drawn  lines  of 
constant  quality  (such  as  a-b)  or  constant  superheat  (such  as  c-d)  and  lines 
of  constant  pressure  (such  as  e-f  or  g-h)  which  are,  of  course,  lines  of 
constant  temperature  in  that  portion  of  the  diagram  which  represents 
the  properties  of  wet  steam.  On  this  diagram,  vertical  lines  are  lines  of 
constant  entropy  and  are  therefore  adiabatic  lines.  Horizontal  lines 
are  lines  of  constant  total  heat.  Any  point  on  the  diagram  is  determined 


ART.  349    THE  TOTAL  HEAT-ENTROPY  OR  MOLLIER  DIAGRAM         385 


by  the  intersection  of  four  lines,  namely  a  constant  total  heat  line  (hor- 
zontal)  a  constant  entropy  line  (vertical) ,  a  constant  pressure  line  (diag- 
onal) and  a  constant  quality  or  superheat  line  (sloping) .  If,  for  instance, 
the  pressure  and  quality  of  steam  are  known,  its  total  heat  and  entropy 
may  be  determined.  For  instance,  point  ra  is  the  state  point  on  this 
diagram  of  steam  of  21  pounds  pressure  and  80  per  cent  quality.  The 
ordinate  to  this  point  gives  the  total  heat  of  the  steam  (967  B.  T.  U.),  and 
the  abscissa  its  entropy  (1.45).  If  any  two  of  the  four  properties  are 
known,  the  other  two  may  be  determined  from  the  diagram. 


1300 


800 


1.40 


1.50 


1.60 


1.70 
Entropy 


1.80 


1.90 


FIG.  214. 


In  order  to  use  such  a  diagram  in  the  solution  of  problems,  it  is  con- 
venient to  paste  the  diagram  on  a  well-seasoned  drawing  board,  and  to 
cover  it  with  a  sheet  of  transparent  celluloid,  mounting  it  carefully,  so 
that  its  coordinates  are  vertical  and  horizontal. 

By  graphical  construction  upon  such  a  diagram,  many  problems 
may  be  solved  very  quickly.  For  instance,  let  it  be  assumed  that  in  a 
throttling  calorimeter  the  temperature  and  pressure  of  the  steam  are 
those  shown  by  point  J  (this  would  be  possible  in  case  the  calorimeter 
were  connected  to  a  condenser  in  order  to  increase  the  permissible  wetness 
of  the  steam  to  be  tested).  By  drawing  through  J  a  horizontal  (i.e.,  a 
constant  total  heat)  line,  the  intersection  of  this  line  with  the  pressure 
line  of  the  steam  in  the  pipe  from  which  the  sample  was  taken  (as  at  i}, 
will  give  the  state  point  of  that  steam,  and  its  quality  will  be  known. 


386  ENTROPY   DIAGRAMS  ART.  350 

In  like  manner  if  point  k  be  assumed  to  be  the  state  point  of  the  steam 
entering  a  nozzle,  as  determined  from  its  pressure  and  superheat,  a  vertical 
(i.e.,  an  adiabatic)  line  drawn  to  intersect  the  pressure  line  which  repre- 
sents the  pressure  of  the  steam  as  it  issues  from  the  nozzle,  will  determine 
the  properties  of  steam.  If  point  I  is  at  the  intersection  of  the  adiabatic 
and  the  terminal  pressure  line,  it  is  the  state  point  of  the  issuing  steam. 
The  length  k-l  will  then  represent  the  heat  transformed  into  kinetic  energy, 
and  by  transferring  the  distance  to  the  velocity  scale  at  the  left  of  Marks 
and  Davis'  diagram,  the  velocity  may  be  read  off  directly,  the  final 
velocity  being  determined  by  the  distance  from  the  initial  velocity  of  the 
steam  entering  the  nozzle.  Other  constructions  will  readily  suggest 
themselves  to  the  reader  for  solving  various  problems  in  connection  with 
the  properties  of  steam  or  its  behavior  in  engines  and  turbines.' 

350.  Temperature-Entropy  Diagrams  for  Hot-air  Engines.  The  tem- 
perature-entropy diagram  may  be  used  to  illustrate  the  action  of  the  work- 
ing fluid  in  a  hot  air  engine.  In  Fig.  215  will  be  found  the  temperature- 
entropy  diagram  of  a  Joule  cycle  engine. 
The  line  d  a  represents  the.  adiabatic  com- 
pression of  the  working  fluid,  the  line  a-b  the 
increase  in  entropy  and  temperature  which 
occurs  in  the  heater,  the  line  b—c  represents  the 
adiabatic  expansion  of  the  working  fluid,  and 
the  line  c-d,  the  decrease  in  temperature  and 
entropy  which  occurs  in  the  cooling  chamber. 
Lines  a-b  and  d—c  will,  of  course,  be  logarithmic 
curves,  since  the  specific  heat  of  the  gas  is  con- 
stant. The  quantity  of  heat  supplied  is  repre- 
sented by  the  area  /  a  b  e,  the  quantity  of 
work  done  by  the  area  abed  and  the  heat 
FlG  215.  rejected  by  the  area  d  c  e  f.  It  will  be  seen  that 

the  efficiency  of  the  cycle  will  be  increased  by 

increasing  the  temperature  range  during  the  adiabatic  expansion  or 
compression  and  that  the  lower  the  initial  temperature  at  the 
beginning  of  adiabatic  expansion,  the  greater  will  be  the  efficiency  of 
the  cycle. 

No  temperature-entropy  diagram  can  be  drawn  for  a  Stirling  cycle 
engine,  since  the  conditions  of  operation  of  the  engine  are  contrary  to  the 
fundamental  assumption  made  in  drawing  a  temperature-entropy  diagram. 
In  the  Stirling  engine,  a  portion  of  the  working  fluid  is  at  the  temperature 
of  the  heater  while  the  remainder  of  it  is  at  the  temperature  of  the  cooler. 
The  temperature-entropy  diagram  assumes  that  the  entire  quantity  of 
the  working  fluid  is  at  the  same  temperature,  consequently  no  tempera- 
ture-entropy diagram  can  be  drawn  for  this  engine. 


f 


ART.  351 


DIAGRAM   OF  THE  OTTO  CYCLE 


387 


351.  The   Temperature-Entropy   Diagram   of    the  Otto    Cycle.     The 

temperature-entropy  diagram  of  the  Otto  cycle  may  be  seen  in  Fig.  216. 
It  is  bounded  by  two  adiabatics,  a-b  and  c-d,  and  two  constant-volume 
lines  b—c  and  a-d.  These  lines  are,  of  course,  logarithmic  curves.  It  is 
assumed  that  the  specific  heat  of  the  working  fluid  is  constant.  The  heat 
supplied  is,  of  course,  the  area  b-c-e-f,  and  the  work  done  is  the  area 
bed  a,  and  its  heat  rejected  is  area  fa  d  e. 

352.  Temperature-Entropy  Diagram  of  other  Gas-engine  Cycles.    The 
temperature-entropy  diagram  of  the  Sargent  cycle  may  be  found  in  Fig. 
217.     a-b  and  c-d  are  adiabatics,  b-c  is  a  constant-volume  line,  d-e  is  a 


Of 

FIG.  216. 


constant- volume  line  and  e-a  is  a  constant-pressure  line.  The  heat  supplied 
is  b  c  f  g  and  the  work  done  b  c  d  e  a.  The  extra  power  gained  over  the 
Otto  cycle  is  represented  by  the  area  d'  a  e  d,  line  a-d'  being  a  constant 
volume  line. 

The  temperature-entropy  diagram  of  the  Diesel  cycle  with  isothermal 
expansion  is  seen  in  Fig.  218.  Lines  a-b  and  c-d  are  adiabatics,  b-c  is  an 
isothermal,  and  d-a  a  constant-volume  line.  In  Fig.  219  is  seen  the 
temperature-entropy  diagram  of  the  Diesel  cycle  with  isobaric  expansion. 
a-d  and  c-b  are  adiabatics,  d-c  is  the  isobaric  line  and  b-a  the  constant- 
volume  line.  It  will  be  seen  that  by  increasing  the  temperature  range  by 
isobaric  instead  of  isothermal  expansion,  the  theroretical  efficiency  of  the 
cycle  is  increased. 

353.  The  Actual  Temperature-Entropy  Diagram  of  an  Otto  Engine. 
The  form  of  temperature-entropy  diagram  which  will  actually  be 
given  by  an  Otto  cycle  engine  may  be  seen  in  Fig.  220.  The  line  a-c  is 


388 


ENTROPY   DIAGRAMS 


ART.  353 


the  actual  compression  line.  The  line  c-x,  which  is,  of  course,  approximately 
a  logarithmic  curve,  represents  the  rise  in  temperature  at  explosion. 
The  line  x-t  is  the  expansion  line  and  the  line  t-a  represents  the  fall  in 
pressure  at  the  end  of  expansion.  This  diagram  is  shown  superimposed 
upon  the  diagram  a  c'  x'  tf ,  which  is  the  theoretical  temperature-entropy 
diagram  for  an  Otto  cycle  engine  when  the  quantity  of  heat  added  at 
explosion  is  the  entire  quantity  of  heat  contained  in  the  working  fluid. 
The  diagram  a  c'  x"  t"  is  the  theoretical  temperature-entropy  diagram  of 
the  Otto  cycle  for  the  same  temperature  limits  as  occur  in  the  actual 
engine. 

It  will  be  noted  that  the  actual  compression  line  a-c  at  first  runs  to  the 
right  and  then  turns  off  to  the  left.     The  reason  for  this  is  that  during 


-N— 


FIG.  218. 


i        e 
FIG.  219. 


the  early  part  of  the  compression  stroke  the  temperature  of  the  walls  is 
higher  than  that  of  the  working  fluid,  the  working  fluid  receives  heat  from 
the  walls,  and  its  entropy  is  increasing.  The  working  fluid  soon  becomes 
hotter  than  the  walls,  however,  and  begins  to  lose  heat  to  them,  so  that 
its  entropy  decreases  during  the  latter  portion  of  the  compression  stroke. 
During  the  explosion  the  working  fluid  is  receiving  heat  on  account  of 
the  combustion  of  the  charge,  and  is  losing  heat  to  the  cylinder  walls. 
The  line  c-x  represents  the  net  effect  of  the  addition  and  abstraction  of 
the  heat  during  this  period.  During  the  expansion  period  the  working 
fluid  is  receiving  heat  on  account  of  the  delayed  combustion  of  the 
charge,  and  it  is  also  losing  heat  to  the  cylinder  walls.  On  the  whole 
the  quantity  of  heat  lost  to  the  walls  is  greater  than  that  received  from 


ART.  354 


I  HE   AIR  COMPRESSOR 


389 


the  combustion  of  the  charge, 
so  that  the  expansion  line  tends 
to  the  left  as  it  descends.  The 
line  t-a  is  of  course  identical  with 
the  theoretical  line. 

The  exact  form  of  tempera- 
ture-entropy diagram  given  by 
an  Otto  cycle  engine  will  vary 
with  the  size  of  the  engine,  the 
character  of  the  charge,  and  the 
relative  amounts  of  the  several 
losses.  The  temperature-entropy 
diagram  is  not  as  useful  in  ana- 
lyzing the  losses  occurring  in  a 
gas  engine  as  it  is  in  analyzing 
those  in  a  steam  engine,  and  care 
must  be  taken  when  employing 
the  diagram  to  see  that  the  quan- 
tities of  heat  represented  on  the 
diagram  are  properly  interpreted. 
354.  The  Air  Compressor. 
No  temperature-entropy  diagram 
can  be  drawn  for  an  air-com- 
pressor cycle,  since  the  quantity 

of  working  fluid  contained  in  the  cylinder  is  not  constant.  It  might  be 
thought  that  the  diagram  could  be  constructed  by  drawing  two  adiabatics 
and  two  constant-pressure  lines  for  air,  but  it 
must  be  borne  in  mind  that  the  air  is  expelled 
from  the  cylinder  at  constant  temperature  as  well 
as  at  constant  pressure.  The  constant-pressure 
line  of  the  temperature-entropy  diagram  assumes 
that  the  weight  of  the  working  fluid  is  constant, 
and  that  its  volume  is  decreased  by  changing  its 
temperature.  It  will  be  seen  then  that  a  tem- 
perature-entropy line  diagram  cannot  be  drawn, 
since  the  working  fluid  does  not  perform  a  true  cycle. 
355.  The  Temperature-Entropy  Diagram  of 
Refrigerating  Machines.  The  theoretical  tempera- 
ture-entropy diagram  for  a  refrigeration  cycle  is 
similar  in  its  general  appearance  to  that  of  a  heat- 
engine  cycle.  The  temperature-entropy  diagram  of 
—  —  the  reversed  Joule  cycle  may  be  seen  in  Fig.  221. 
FIG.  221.  I^ne  a~b  represents  the  absorption  of  the  quantity 


FIG.  220. 


a 


390 


ENTROPY   DIAGRAM'S 


ART.  355 


of  heat  measured  by  the  area  /  a  b  e  in  the  vaporizer,  which  raises  the  tem- 
perature of  the  working  fluid  from  point  a  to  point  b  and  increases  its 
entropy.  Adiabatic  compression  then  increases  its  temperature  to  point 
c  without  changing  its  entropy.  The  line  c-d  represents  the  process  of 
cooling  the  working  fluid  in  the  condenser  at  constant  pressure,  during  which 
time  it  parts  with  the  quantity  of  heat  represented  by  the  area  feed. 
The  area  feed  represents  the  heat  taken  from  the  vaporizer,  /  e  b  a,  plus 
the  work  done  upon  the  working  fluid,  abed. 

The  temperature-entropy  diagram  of  the  ammonia-compression  cycle 
may  be  seen  in  Fig.  222.     At  point  a  compression  of  dry  and  saturated 

ammonia  vapor  begins.  The 
ammonia  vapor  in  practice 
may  be  slightly  wet  or  slightly 
superheated,  but  it  is  usually 
nearly  dry  and  saturated. 
This  vapor  is  compressed 
adiabatically  along  the  line 
a-b  and  becomes  superheated 
during  the  process.  The  super- 
heated vapor  is  introduced  into 
the  condenser  where  it  is  con- 
densed at  constant  pressure 
(after  being  cooled  to  the 
saturation  temperature)  along 
the  constant-pressure  line 
b-c-d.  In  passing  through 
the  expansion  valve,  the  total 
heat  of  the  ammonia  vapor  is 
unchanged,  and  the  fall  in 
temperature  is  therefore  repre- 
sented by  the  constant  total 
heat  line  d-e.  The  entropy  of 

evaporation  of  that  portion  of  the  liquid  which  is  evaporated  by  the  heat 
of  the  liquid,  is  represented  by  the  segment  0—e.  The  remainder  of 
the  latent  heat  of  evaporation  is  taken  from  the  vaporizer  at  constant 
temperature,  the  process  being  represented  by  the  line  e-a.  The  heat 
abstracted  from  the  vaporizer  is,  of  course,  represented  by  the  area  g  e  a  /, 
while  the  heat  rejected  to  the  condenser  is  equal  to  the  area  g  e  d  c  b  f. 

The  actual  temperature-entropy  diagram  which  would  be  obtained 
from  an  ammonia  compression  plant  may  be  seen  in  Fig.  223.  The  vapor 
that  comes  to  the  compressor  is  usually  slightly  wet.  Since  the  cylinder  of 
the  machine  is  warmer  than  the  vapor  which  it  compresses,  this  vapor 
is  almost  immediately  dried  and  then  continues  to  gain  heat  during  the 


ART.  355  DIAGRAM    FOR  REFRIGERATING  MACHINES 


391 


FIG.  22:?. 


most  of  the 'compressed  period. 

The  remainder  of  the  diagram 

is  identical  with  the  theoretical 

diagram,  but   the   compression 

line    a-b    is    approximately   of 

the    form    shown.      Since    the 

ammonia  vapor  is  not  entirely 

dry  as  it   enters  the   cylinder, 

the  amount  of  heat  abstracted 

from  the  vaporizer  per  pound 

of    working    fluid,    represented        , 

by  the  area  g  e  a  /,  is  less  than 

would    be    transferred    if    the 

ammonia    were    dry.      At    the 

same  time,  the  amount  of  work 

required  to  compress  the  am- 
monia and  deliver  it  into  the 

condenseris  considerably  greater 

than  it   was  in  the  theoretical 

cycle,    since    the    vapor   gains 

heat  during  the  early  part  of 

the    compression    period    from 

the    walls   of  the    compressor    cylinder.      The    efficiency  of   the   system 

is,  of  course,  equal  to  the  area  g  e  a  f  divided  by  the  area  e  d  c  b  a. 

The  temperature-entropy  dia- 
gram for  an  absorption  system 
may  be  seen  in  Fig.  224.  In  this 
diagram,  line  a-b  represents  the 
vaporization  of  the  ammonia  at  con- 
stant pressure  in  the  generator,  while 
line  b-a  (the  same  line  reversed) 
represents  its  condensation  in  the 
condenser.  The  ammonia  liquid  now 
escapes  through  the  expansion  valve, 
a  process  represented  by  the  con- 
stant total  heat  line  a-c.  Within 
the  vaporizer,  the  remainder  of  the 
liquid  evaporates,  a  process  repre- 
sented by  the  evaporation  line  c-d. 
This  ammonia  is  then  superheated  by 
absorbing  heat  at  constant  pressure 
along  the  line  d-e.  It  then  con- 
FIG.  224.  denses  by  absorption  in  water  and 


\ 


g   fc 


392  ENTROPY  DIAGRAMS  ART.  355 

the  heat  is  removed  from  the  absorber  at  constant  temperature,  that  process 
being  represented  by  the  line  e-f.  Its  temperature  is  now  raised  by  the 
application  of  heat  until  the  liquid  is  sufficiently  hot,  so  that  the  ammonia 
may  be  vaporized.  The  heat  absorbed  in  the  vaporizer  is  represented 
by  the  area  c  d  g  h.  The  heat  supplied  to  the  generator  is  represented  by 
the  area  I  a  b  i.  The  heat  taken  from  the  absorber  is  represented  by  the 
area  j  f  e  k.  The  heat  represented  by  the  area  /  /  a  I  is  returned  by  the 
regenerator  coil,  from  the  spent  liquid  entering  the  absorber,  to  the  liquid 
entering  the  generator.  The  quantity  of  heat  absorbed  by  the  condenser 
is  represented  by  the  area  I  a  b  i. 

In  drawing  this  diagram  it  has  been  assumed  that  the  heat  added  or 
abstracted  was  the  latent  heat  of  ammonia  vapor.  Since,  however, 
ammonia  has  an  affinity  for  water,  additional  quantities  of  heat  are 
transferred,  due  to  the  extra  heat  required  to  evaporate  ammonia  from  an 
aqueous  solution.  No  account,  however,  has  been  taken  of  these  quan- 
tities in  this  diagram. 


CHAPTER  XXVI 
THE   KINETIC  THEORY  OF  HEAT 

356.  The  Kinetic  Theory  of  Gases.    All  of  the  phenomena  noted  in  the  first  seven 
chapters  of  this  book,  and  collectively  termed  the  properties  of  gases  and  vapors  and 
their  mixtures,  may  be  entirely  explained  by  the  kinetic  theory  of  heat.     This  theory 
assumes  that  any  mass  of  gas  or  dry  vapor  is  composed  of  a  great  number  of  very  small 
particles.     These  particles  are  perfectly  elastic,  and  in  the  case  of  a  perfect  gas,  exert 
no  force  upon  anything  with  which  they  are  not  in  actual  contact.     In  the  case  of 
imperfect  gases,  these  particles  tend  to  attract  or  repel  one  another.     The  mass  of 
each  particle,  although  minute,  is  definite  and  unchangeable.     The  volume  of  each 
particle  is  infinitesimal  in  the  case  of  a  perfect  gas.     In  the  case  of  an  imperfect  gas, 
the  volume  is  finite,  although  extremely  minute.     In  case  the  gas  is  of  homogeneous 
composition,  each  of  the  particles  is  exactly  like  every  other.     These  particles  are  in 
chemistry  termed  molecules,  and  hereafter  in  this  chapter  will  be  designated  by  that 
term. 

Assume  that  a  number  of  such  molecules  are  confined  within  the  walls  of  a  vessel; 
and  that  these  walls  are  motionless  and  absolutely  rigid.  Eac*h  particle,  once  it  is 
set  in  motion,  will  move  with  uniform  velocity  in  a  right  line  until  it  impinges  upon 
one  of  the  walls.  Since  it  is  perfectly  elastic,  and  the  wall  is  perfectly  rigid,  it  will 
rebound  from  the  wall  with  undiminished  velocity  and  unchanged  energy.  It  will 
proceed  in  its  path  until  it  encounters  a  second  wall,  from  which  it  will  rebound  in  the 
same  manner,  and  will  continue  thus  to  travel  in  straight  lines  from  wall  to  wall  with 
unchanged  velocity.  Each  of  the  particles  contained  in  the  vessel  will  behave  in  the 
same  manner,  arid  since  they  are  assumed  to  be  infinitesimal  in  size,  they  will  encounter 
each  other  only  at  infinite  intervals.  As  the  result  of  the  impact  upon  the  walls  of  the 
vessel,  these  walls  will  experience  a  pressure  whose  amount  we  will  now  determine. 

357.  Pressure  Exerted  on  Account  of  the  Motion  of  the  Molecules.     Assume 
that  the  vessel  is  a  cube  bounded  by  six  planes,  each  1  foot  square.    It  will  then  contain 
1    cubic    foot   of    gas.     Assume    that  this   volume   contains  a  molecule  whose  mass 
is  m,  and  whose  velocity,  normal  to  a  given  face,  is  Vl  feet  per  second.     Since  the 
distance  from  the  given  face  to  the  opposite  face  and  back  is  2  feet,  the  molecule 

V 
will    strike  the  given  face  —  times  per  second.     Each  time  it  strikes  the  face  its 

momentum  is  changed  by  the  amount  2mVl.  Each  second,  the  given  face  will  change 
the  momentum  of  the  molecule  by  the  amount  m  TV-  The  rate  of  change  of  momentum 
is  numerically  equal  to  the  force  producing  the  change.  Hence  the  mean  value  of  the 
force  exerted  by  the  face  in  resisting  the  impacts  of  this  molecule  is  m  V^. 

If  the  space  contains,  in  addition,  a  second  molecule  having  the  same  mass,  and 
whose  velocity  normal  to  the  given  plane  is  Y2>  then  the  force  exerted  by  the  impacts 
of  the  two  molecules  will  be  ra(TV  +  TV),  and  so  on  for  any  number  of  molecules. 
Finally,  if  the  space  contains  n  molecules,  the  force  exerted  by  their  impacts  upon 
the  face  will  be  • 

+...  +  V$ •  .     .    .     .     (1) 

393 


394  THE   KINETIC   THEORY   OF  HEAT  ART.  358 

Designating  the  product  of  w  and  n  by  M,  and 


n 
we  will  have  for  the  pressure  in  pounds  per  square  foot  exerted  by  the  gas 

P=  MVI (2) 

In  the  case  of  an  actual  gas  under  an  appreciable  pressure  the  molecules  are  very 
great  in  number  and  are  traveling  in  all  directions.  The  value  of  \' ^  is  therefore  the 
same  for  each  of  the  six  faces  of  the  cube.  The  square  of  the  velocity  of  each  particle 
is  the  sum  of  the  squares  of  the  velocity  components  normal  to  each  of  three  adjacent 
faces.  Consequently,  the  mean  of  the  squares  of  the  velocities  of  all  the  molecules 
is  three  times  the  mean  of  the  squares  of  any  component  of  the  velocities.  We  may 
therefore  write 

V2  =  3  V,; (3) 

Replacing  Vn   by  -y> 

W 

and  M  by  —  in   equation  (2),  we  will  have 
9o 

WV2 


in  which  W  is  the  weight  of  the  gas  in  pounds  per  cubic  foot,  V2  is  the  mean  of  the  squares 
of  the  velocities  of  all  the  molecules,  and  g0  is  the  standard  acceleration  of  gravity. 
Since  the  weight  of  the  gas  per  cubic  foot  is  equal  to  the  weight  per  molecule  (w) 
multiplied  by  the  number  of  molecules  per  cubic  foot  (w)  we  may  write  the  above 
equation  in  the  form 


wV2 
In  the  above  expression,  -^ —  is  of  course  the  mean  kinetic  energy  per  molecule  of  the 

gas.  Hence  the  pressure  of  the  gas  is  proportional  to  the  mean  kinetic  energy  per 
molecule,  and  to  the  number  of  molecules  per  unit  of  volume.  Substituting  ^  V  for 
Vn  m  equation  (2),  we  will  have 

P  =  JMV2, -     -     (6) 

when  the  mass  of  gas  M  occupies  one  cubic  foot.  If  it  occupies  V  cubic  feet,  we  will 
have 

PV^MV\ (7) 

in  which  P  is  the  pressure  of  the  gas  in  pounds  per  square  foot,  V  is  the  volume  of  the 

gas  in  cubic  feet,  M  is  the  mass  of  the  gas  in  kinetic  mass  units,  and  is  equal  to  — ,  where 

yo 

W  is  its  weight  in  pounds,  and  V   is  the  mean  of  the  squares  of  the  molecular  velocities. 

358.  Te  nj>jr  liu  e  of  a  Gas  Proportional  to  the  Mean  Kinetic  Energy  of  the 
Molecules.  If  W3  increase  the  mean  kinetic  energy  per  molecule,  we  must  do  so  by 
transferring  energy  to  the  gas.  If  we  assume  that  this  energy  is  transferred  to  the  gas 
in  the  form  of  heat,  we  will  have  the  mean  kinetic  energy  per  molecule  increased  by 


AET.  359  LOSS  OF  ENERGY  DURING   EXPANSION  395 

the  addition  of  heat.  We  know  that  the  addition  of  heat  to  a  gas  increases  its  temper- 
ature and  pressure,  and  if  the  gas  be  perfect,  the  increase  in  temperature  and  pressure 
is  proportional  to  the  quantity  of  heat  added.  Hence  we  may  conclude  that  the 
absolute  temperature  as  well  as  the  pressure  of  any  gas  given  is  proportional  to  the 
mean  kinetic  energy  per  molecule. 

A  further  inspection  of  equation  (5)  in  the  preceding  article  will  show  that  if  we 
change  the  mass  of  a  molecule  without  changing  the  number  of  the  molecules,  that  the 
pressure  of  the  gas  will  be  the  same  when  V  is  so  changed  as  to  make  the  mean  kinetic 
energy  per  molecule  the  same.  Certain  chemical  phenomena  point  to  the  conclusion 
that  the  number  of  molecules  in  a  given  volume  of  gas  confined  at  a  given  pressure  and 
temperature  is  always  the  same  whatever  be  the  nature  of  the  gas.  Hence,  we  arrive 
at  the  conclusion  that  the  absolute  temperature  of  any  gas  is  proportional  to  the 
mean  kinetic  energy  per  molecule. 

When  a  cubic  foot  of  gas  is  heated  at  constant  volume,  the  heat  will  be  entirely 
expended  in  increasing  the  velocity  of  the  molecules.  Consequently,  the  heat  imparted 
to  the  gas,  when  measured  in  dynamic  units,  will  be 

MTV      MFi2 
//#„  =  ——      — — (8) 

in  which  F22  is  the  mean  of  the  square  of  the  final  molecular  velocities,  and  V\2  is 
the  mean  of  the  squares  of  the  initial  velocities.  This  equation  may  be  written 


359.  Loss  of  Energy  during  Expansion.  When  the  gas  is  heated  at  constant  pres- 
sure, a  part  of  the  energy  is  expended  in  doing  external  work.  If  we  assume  that  all 
of  the  energy  is  first  transferred  to  the  molecules,  then  some  of  this  energy  will  be  sur- 
rendered by  the  molecules  during  their  impact  upon  the  moving  wall  of  the  expanding 
vessel.  The  increase  in  volume  of  the  gas  is  proportional  to  the  absolute  temperature 
and  is  consequently  proportional  to  the  change  in  the  mean  square  of  the  velocity 
of  the  moelcules.  The  work  done  by  the  gas  is  found  by  multiplying  the  initial  pres- 
sure by  the  change  in  volume.  Since  the  initial  volume  is  1  cubic  foot,  and  the 
volumes  are  proportional  to  the  mean  of  the  squares  of  the  velocities  of  the  molecules, 
we  will  have  for  the  change  in  volume 


For  the  pressure  of  the  gas  we  will  have  the  value 

D     mV*     2n 


Multiplying  (10)  and  (11)  together  we  will  have  for  the  work  of  expansion 

PJF=(F22-F12)f (12) 

The  increase  in  the  kinetic  energy  of  the  molecules  is  given  by  equation  (9),  Art. 
358.  Adding  this  to  equation  (12),  we  will  have  for  the  energy  required  to  heat  a 
cubic  foot  of  the  gas  at  constant  pressure 


396  THE  KINETIC  THEORY  OF  HEAT  ART.  360 

The  quantity  of  energy  given  by  equation  (y)  Art.  358,  is  proportional  to  the 
specific  heat  of  the  gas  at  constant  volume.  That  given  by  equation  (13),  is  propor- 
tional to  the  specific  heat  of  the  gas  at  constant  pressure.  Dividing  the  latter  by 
the  former  we  will  have  for  the  ratio  of  the  specific  heats 

5M     M 

-Q-+-2=l%  =  r (14) 

We  may  therefore  conclude  from  equation  (14)  that  the  value  of  f  for  a  gas  whose 
molecules  have  translational  energy  only,  is  always  If. 

360.  Intra-molecular  Energy.  The  molecules  of  a  gas  will  have  translational 
energy  only,  when  each  of  the  molecules  consists  of  one  particle  wrhose  dimensions  are 
infinitesimal.  Such  a  gas  is  said  to  be  monatomic.  If  the  molecule  is  composed  of  two 
or  more  particles  (in  chemistry  termed  atoms)  with  a  finite  distance  between  them,  it 
will  be  apparent  that  they  must  have  a  motion  relative  to  one  another,  which  will 
absorb  a  portion  of  the  heat  energy  imparted  to  the  molecule.  Such  a  gas  is  said  to  be 
polyatomic.  The  energy  which  the  molecule  contains  in  virtue  of  the  relative  motion 
of  its  atoms  is  termed  intramolecular  energy.  The  energy  which  it  contains  in  virtue 
of  its  mass  and  the  velocity  of  its  center  of  gravity,  is  termed  translational  energy.  The 
sum  of  the  intramolecular  and  translational  energy  of  the  molecule  is  termed  the 
intrinsic  energy.  Clausius  has  shown  that  the  ratio  of  the  mean  intramolecular  energy 
to  the  mean  translational  energy  is  a  constant  for  any  gas.  This  ratio  is  therefore 
called  Clacsius'  ratio,  and  is  designated  by  the  letter  p. 

The  energy  which  must  be  imparted  to  the  gas  for  the  purpose  of  increasing  its 
temperature  will  be  1  -f  p  times  that  which  would  be  required  by  the  same  volume 
of  a  monatomic  gas.  We  will  have  then  for  the  quantity  of  energy  imparted  to  the 
gas  in  heating  it,  at  constant  volume, 


Adding  equation  (15)  to  equation  (12)  of  the  preceding  article,  we  will  have  the  energy 
imparted  to  the  gas  to  heat  it  at  constant  pressure,  which  is 


JHP  = 


5  +  3/7 
3 


Dividing  16   by  15  we  will  have 


5  +  3  p 


r="-^-- (17) 

3-r3,o 

It  may  be  noted  that  when  p0  becomes  zero,  the  value  ?  becomes  | -,  as  it  should.  Solving 
(17)  for  p,  we  will  have  for  the  value  of  Clausius'  ratio  for  a  gas  for  which  the  constant 
f  is  known, 

P  =  ^^-  (18) 


361.  Adiabatic  Expansion  of  Gases.  When  a  gas  is  confined  within  an  expanding 
vessel,  for  instance,  a  cylinder  having  a  moving  piston,  the  mean  intrinsic  energy  per 
molecule  will  diminish,  since  the  molecules  which  strike  the  piston  will  rebound  from 
its  face  with  diminished  absolute  velocity,  their  velocity  relative  to  the  face  of  the  piston 
being  unchanged  in  amount  and  reversed  in  direction  by  the  impact.  The  energy 
thus  surrendered  by  the  molecules  reduces  their  mean  kinetic  energy  and  so  reduces 
the  temperature  of  the  gas.  In  case  the  volume  of  the  cylinder  is  diminished,  the  mole- 


ART.  362  CONDITION  OF  EQUILIBRIUM  397 

cules  will  rebound  from  the  moving  piston  with  increased  velocity,  the  velocity  relative 
to  the  face  again  being  the  same  after  impact  as  before.  The  result  of  such  compres- 
sion is,  of  course,  to  increase  the  mean  kinetic  energy  per  molecule  and  the  temperature 
of  the  gas.  The  phenomena  of  adiabatic  expansion  and  compression  are  thus  fully 
explainable  by  the  kinetic  theory. 

362.  Condition  of  Equilibrium  between  Molecules  of  Different  Masses.  If  a 
gas  be  conceived  to  consist  of  molecules  of  two  different  kinds  (i.e.,  if  it  is  a  mixture  of 
different  gases)  the  molecules  will  pass  among  each  other  and  occasionally  molecules 
of  one  kind  will,  by  collision  or  otherwise,  exert  force  upon  molecules  of  the  other  kind. 
Each  time  that  force  is  exerted  between  two  molecules  of  different  kinds,  they  will 
exchange  a  portion  of  their  kinetic  energy.  In  general,  the  molecule  having  the  greater 
kinetic  energy  will  give  up  a  portion  of  its  energy  to  the  molecule  having  less  energy, 
so  that  as  a  result  of  the  continued  interchange  of  energy,  we  will  find  that  the  mean 
kinetic  energy  per  molecule  of  the  two  different  kinds  of  molecules  will  become  equal, 
or  in  other  words,  the  two  constituents  of  the  mixture  will  come  to  the  same 
temperature. 

In  the  case  of  such  mixtures,  the  mean  velocities  of  the  different  classes  of  mole- 
cules will  be  different.  In  order  that  the  temperature  of  the  two  constituents  shall  be 
the  same,  the  mean  value  of  the  kinetic  energy  per  molecule  must  be  the  same  for  the 
several  constituents.  In  order  to  make  this  true,  it  is  necessary  that  the  mean  square 
of  the  velocities  of  each  kind  of  molecules  shall  be  inversely  proportional  to  the  mass  of 
a  molecule  of  that  kind,  so  that  the  lighter  molecules  in  a  mixture  will  have  high 
velocities  while  the  heavier  ones  will  have  low  velocities.  We  have  already  seen  in 
equation  (7)  Art.  357,  that  P  F  =  £  MV2',  this  equation  may  be  \vritten 

PV-^V' (19) 

Substituting  the  value  of  P  V  from  the  characteristic  equation  of  gases,  we  will  have, 
=  W  R  T,  whence  we  deduce  that 


vV2  =  V3</A:7'. C-'o) 

which  is  an  equation  giving  the  value  of  the  square  root  of  the  mean  square  of  the 
velocities  of  the  molecules  of  the  gas.  Substituting  the  proper  values  in  this  equation 
we  will  find  that  the  velocity  of  air  molecules  at  70°  F.  will  average  about  1650  feet  per 
second,  while  that  of  hydrogen  molecules  at  the  same  temperature  will  average  about 
6250  feet  per  second.  It  will  be  seen  that  the  average  velocities  of  these  molecules 
is  quite  high  and  a  small  proportion  of  them  will  have  velocities  far  exceeding  these 
average  velocities.  In  case  the  velocity  of  a  molecule  exceeds  about  35,000  feet  per 
second,  it  will  be  carried  beyond  the  sphere  of  the  earth's  attraction.  It  will  thus  be 
seen  that  the  tendency  will  be  for  the  lighter  gases  to  gradually  escape  from  the  earth's 
atmosphere.  Were  the  value  of  the  attraction  of  gravitation  sufficiently . reduced, 
as  it  is  in  the  case  of  the  smaller  heavenly  bodies,  the  escape  of  gases  would  be  made 
much  easier,  so  that  those  bodies  which  are  small  as  compared  with  the  earth  will  have 
no  atmosphere.  The  moon  is  such  a  body. 

363.  The  Flow  of  Gas  from  a  Vessel  through  an  Orifice.  Assume  two  vessels  to  be 
separated  from  one  another  by  a  partition.  Assume  that  the  right-hand  vessel  is  filled 
with  gas  and  that  the  left-hand  vessel  is  empty.  If  now  a  small  opening  be  made  in 
the  partition,  a  part  of  the  gas  will  pass  from  the  right-hand  vessel  into  the  left-hand 
vessel,  until  the  pressures  are  equalized.  The  molecules  contained  in  the  right-hand 
vessel  do  not  all  have  the  same  velocity,  some  of  them  having  higher  velocities  than 


398  THE  KINETIC  THEORY  OF  HEAT  AKT.  364 

others.  Those  having  the  higher  velocities  will  rebound  from  the  walls  more  often  than 
do  the  others,  and  hence  will  have  a  better  chance  of  passing  through  the  opening. 
Consequently,  after  the  gas  has  flowed  from  the  right  to  the  left,  those  molecules 
contained  in  the  left-hand  vessel  will  on  the  average  have  higher  velocities  than  those 
contained  in  the  right-hand  vessel.  The  pressures  in  the  two  vessels  will  be  equal, 
but  the  temperature  of  the  gas  contained  in  the  left-hand  side  will  be  higher,  and  its 
mass  will  be  less  than  that  of  the  gas  contained  in  the  right-hand  side,  arid  the  total 
energy  (or  heat)  of  the  whole  mass  will  be  unchanged.  In  the  course  of  time  the  entire 
mass  of  gas  will  gradually  come  to  thermal  equilibrium  by  the  passage  of  molecules 
back  and  forth  through  the  orifice,  and  finally  each  vessel  will  be  filled  with  an  equal 
number  of  molecules  having  the  same  mean  energy  per  molecule. 

If  a  current  of  gas  be  caused  to  'flow  through  a  porous  plug,  the  temperature  of  the 
gas  will  be  unchanged,  since  every  portion  of  the  gas  as  it  is  forced  through  the  plug 
remains  together  and  the  molecules  having  different  velocities  are  not  permitted 
to  pass  into  separate  regions.  If  there  are  no  forces  exerted  by  the  molecules  upon 
one  another,  the  mean  kinetic  energy  per  molecule  and  therefore  the  temperature  of 
the  gas  will  remain  unchanged  in  passing  through  such  a  porous  plug. 

364.  Osmosis.     If  a  vessel  to  be  assumed  to  contain  two  kinds  of  gas  mixed  together 
in  equal  proportions,  the  velocities  of  the  molecules  of  the  lighter  gas  will  on  the  average, 
be  much  higher  than  those  of  the  molecules  of  the  denser  gas.     Molecules  having  high 
velocities  will  rebound  more  often  from  the  walls  than  do  the  molecules  having  low 
velocities,  and  consequently  will  have  greater  opportunity  for  passing  through  an 
opening.     If  an  opening  be  made  in  the  wall  of  the  vessel,  the  molecules  of  the  lighter 
gas  will  pass  through  the  openings  more  often  than  do  those  of  the  denser  gas.     If 
the  opening  connects  the  vessel  with  another  similar  but  empty  vessel  in  the  manner 
described  in  the  previous  article,  after  the  pressures  are  equalized  the  gas  contained 
in  the  left-hand  vessel  will  consist  of  a  larger  proportion  of  the  lighter  molecules  than 
does  the  gas  remaining  behind  in  the  right-hand  vessel.     Assume  as  an  illustration 
that  the  right-hand  vessel  at  first  contains  ari  equal  number  of  hydrogen  and  oxygen 
molecules.     The  average  velocity  of  the  hydrogen  molecules  is  four  times  as  great  as 
is  that  of  the  oxygen  molecules,  since  the  weight  of  a  hydrogen  molecule  is  only  TS  of 
the  weight  of  the  oxygen  molecule.     As  a  result,  a  given  area  of  the  wall  will  be  hit 
four  times  as  often    by  a  hydrogen  molecule  as  by  an  oxygen  molecule,  and   four 
molecules  of  hydrogen  will  pass  through  the  opening  for  every  molecule  of  oxygen 
which  passes  through.     The  left-hand  vessel  will  therefore  contain  a  larger  number 
of  hydrogen  molecules  than  of  oxygen  molecules,  after  equilibrium  is  established. 

A  mixture  of  gases  of  different  densities  may  be  partially  separated  by  confining  it 
within  a  porous  vessel.  The  lighter  molecules  will  escape  from  the  vessel  through  the 
pores  in  the  walls  more  quickly  than  do  the  heavier  molecules,  for  reasons  already 
explained.  For  instance,  if  a  quantity  of  hydrogen  and  oxygen  be  confined  indefinitely 
under  pressure  in  a  porous  vessel,  it  will  be  found  eventually  that  the  gas  in  the  vessel 
will  consist  of  four  parts  by  volume  of  oxygen  to  one  part  by  volume  of  hydrogen. 
The  process  of  separating  the  constituents  of  mixtures  of  gases  in  this  manner  is  known 
as  osmosis.  The  same  process  is  employed  for  concentrating  solutions  in  certain 
industries. 

365.  Gases  Confined  in  Conducting  Vessels.     So  far  we  have  been  assuming  that 
the  walls  of  the  vessel  containing  the  gas  have  been  rigid.     This  is  equivalent  to  the 
assumption  that  they  are  non-conductors  of  heat.     If  a  wall  is  not  rigid,  the  effect  of 
the  impact  of  a  molecule  upon  it  will  be  to  cause  the  wall  to  vibrate  and  the  molecule 
will,  as  a  result,  surrender  energy  to  the  wall.     When  the  amplitude  and  rate  of  vibra- 
tion of  the  wall  is  such  that  the  mean  energy  of  the  molecules  is  insufficient  to  increase 
the  vibration,  the  walls  will  have  the  same  temperature  as  the  gas,     If  the  energy  (i.e., 


ART.  366  THE  PROPERTIES   OF  IMPERFECT   GASES  399 

rate  and  amplitude)  of  vibration  of  the  wall  he  increased  by  some  method,  e.g.,  by  the 
application  of  heat  to  the  surface  of  the  containing  vessel,  the  molecules  will,  of  course, 
rebound  from  the  walls  in  the  average  case  with  increased  energy.  This  follows  from 
the  fact  that  if  a  molecule  having  a  given  velocity  normal  to  the  wall  impinges  upon 
the  wall  while  it  is  retreating  with  a  given  velocity,  it  will  lose  twice  this  velocity, 
while  if  it  impinges  upon  an  advancing  wall  having  the  same  velocity,  it  will  gain  twice 
this  velocity.  The  gain  in  energy  in  the  second  case  is  greater  than  the  loss  of  energy 
in  the  first  case.  Consequently  the  temperature  of  a  gas  is  increased  by  incasing  it 
in  walls  hotter  than  the  gas  itself. 

366.  The  Properties  of  Imperfect  Gases.  Thus  far,  we  have  considered  only  those 
gases  in  which  the  molecules  are  of  infmitesmal  size  and  exert  no  force  upon  each 
other  when  they  are  not  in  actual  contact.  Such  gases  are  perfect  gases.  In  the  case 
of  actual  gases,  the  molecules  are  of  finite  size.  Hence  the  gas  behaves  as  if  it  were 
confined  within  a  volume  smaller  than  the  actual  volume  in  which  it  is  confined,  by 
some  proportion  of  the  sum  total  of  the  volumes  of  the  molecules.  \Ve  have  already 
seen  that  the  characteristic  equation  of  a  perfect  gas  is  P  F=  W  R  T.  We  may  write 
then,  on  the  assumption  that  the  molecules  in  W  pounds  of  the  gas  have  a  finite  volume 
whose  effective  value  hi  diminishing  the  actual  volume  of  the  containing  vessel  is 
If  6,  the  equation 

P  (V-Wb)=*WR  T.      .          .......     (21) 

It  is  known  that  the  molecules  of  actual  gases  exert  a  force  one  upon  another. 
This  force  is  in  the  nature  of  an  attraction  which  tends  to  draw  the  molecules  together 
and  therefore  to  reduce  the  pressure  which  they  will  exert  upon  the  walls  of  the  con- 
taining vessel.  Several  equations  have  been  proposed  in  order  to  show  the  effect  of 
this  inter-molecular  attraction  upon  the  behavior  of  the  gas.  The  best  known  is  that 
known  as  Van  der  Waals'  equation,  which  is  usually  written  in  the  form 


(22) 


in  which  P  is  the  pressure  in  pounds  per  square  foot  and  V  is  the  volume  of  1  pound 
of  the  gas,  T  is  its  absolute  temperature,,  and  a  and  b  and  R  are  quantities  depending 
upon  the  nature  of  the  gas.  It  is  usually  assumed  in  works  in  physics  and  physical 
chemistry  that  a,  b  and  R  are  all  constants.  This  is  not  true,  however,  since  the  effect 
on  the  inter-molecular  attraction  upon  the  behavior  of  the  gas  will  depend  upon  the  mass 
of  gas  considered  and  upon  the  form  of  the  containing  vessel.  The  values  of  a  and  b 
will  therefore  vary  according  to  the  circumstances  under  which  the  gas  is  confined. 

On  this  account  Van  der  Waals'  equation  does  not  always  give  concordant  results. 
Clausius  has  therefore  proposed  the  equation 


(23) 


in  which,  R,  a,  b  and  c  are  assumed  to  be  constants,  depending  upon  the  nature  of  the 
gas/  As  in  Van  der  Waals'  equation,  however,  the  values  of  these  quantities  depend 
upon  the  mass  of  the  gas  and  the  form  of  the  containing  vessel,  so  that  the  values 
obtained  experimentally  will  depend  upon  the  circumstances  under  which  the  exper- 
iment was  conducted. 

Clausius  has  shown  that  when  the  molecules  of  a  gas  attract  one  another,  we  may 
write  for  the  characteristic  equation  of  unit  weight  of  the  gas,  the  equation 

MF2=— +*SSflr. ,     (24) 


400  THE   KINETIC   THEORY  OF  HEAT  ART.  367 

In  this  equation  the  value  of  ^  S  £  R  r  has  the  following  meaning:  Let  r  be  the  distance 
between  any  two  molecules  of  the  mass  of  gas  and  R  the  force  which  they  exert  upon 
one  another.  Each  of  the  molecules  exerts  a  force  upon  every  other  one,  so  that  the 
sums  of  the  products  of  the  several  forces  each  multiplied  into  the  distance  through 
which  it  is  exerted,  is  represented  by  the  term  £  S  S  R  r. 

It  is  reasonable  to  assume  that  the  force  which  two  molecules  will  exert  upon  one 
another  is  one  of  attraction  and  that  the  amount  of  this  force  is  inversely  proportional 
to  the  square  of  their  distance,  hence  we  may  write 


in  which  R  is  the  force  of  attraction  between  two  molecules,  r  is  the  distance  between 
the  molecules,  and  A;  is  a  constant  depending  upon  the  nature  of  the  gas.     We  will 

k 
have  for  the  term  R  r,  the  value  —  and  for  the  value  of  the  term  t  S  S  #  r  we  may 


substitute  the  expression  —  and  write  the  equation  in  the  form 


(26) 


for  1  pound  of  the  gas.  Now  the  value  of  the  quantity  \  2  2  R  r  will  be  proportional 
to  the  square  of  the  number  of  molecules,  so  that  we  may  write  for  W  pounds  of  the 
gas,  the  expression 

PV  =  $MV*-  ~-  .........     (27) 

In  this  equation,  r  is  proportional  to  the  distance  between  any  pair  of  molecules  and  is, 
therefore,  proportional  to  the  cube  root  of  the  volume  in  which  the  gas  is  confined. 
Writing  this  so  and  taking  account  of  the  effect  of  the  volume  of  the  molecules,  we 
will  have  finally  for  an  expression  giving  the  relation  between  the  pressure,  volume, 
and  temperature  of  an  imperfect  gas 

P(V-Wb)  =  TTJBr-^~,    .......     •     •     (28) 

in  which  6  and  r  are  constants  for  any  given  gas,  and  a  is  a  quantity  which  depends 
upon  the  form  of  the  containing  vessel,  and  the  nature  of  the  gas,  but  is  independent 
of  the  mass  of  the  gas. 

In  general  experiments  upon  gases  are  conducted  in  cylinders  of  unchanging  diam- 
eter but  of  changeable  length,  so  that  the  form  of  the  containing  vessel  is  continually 
changing  during  the  progress  of  the  experiment.  It  cannot  therefore  be  expected  that 
any  rational  equation  can  be  derived  for  the  behavior  of  a  mass  of  gas  in  such  a  vessel. 

367.  The  Phenomena  of  Liquefaction.  When  an  imperfect  gas  is  sufficiently 
cooled  and  compressed,  the  slower  moving  molecules  in  any  region  of  small  extent 
will  be  drawn  together  by  the  attractive  forces,  and  on  account  of  their  low  kinetic 
energy  will  be  unable  to  separate  themselves,  but  will  continue  to  travel  about  the 
common  center  of  attraction  in  an  irregular  orbit  of  some  form.  Wherever  several 
molecules  are  drawn  together  in  this  manner,  a  point  is  produced  at  which  attractive 
forces  are  centered,  so  that  other  molecules  will  be  attracted  toward  that  point.  Those 
having  high  velocities  will  pass  the  point,  while  those  having  low  velocities  will  be 
drawn  into  the  system  and  help  to  increase  its  attractive  force.  When  this  condition 
occurs,  a  gas  begins  to  condense  into  a  liquid.  The  action  will  be  accelerated  by  the 
presence  of  small  particles  of  dust  which  tend  by  their  attraction  to  gather  about 


ART.  368  THE  PHENOMENA   OF  VAPORIZATION  401 

themselves  quantities  of  molecules.  As  fast  as  such  systems  of  molecules  are  formed 
they  are  drawn  together  by  their  attractive  forces  so  that  finally  the  whole  mass  will 
condense  into  a  liquid  provided  that  the  pressure  and  temperature  are  kept  constant. 
In  approaching  these  centers  of  attraction  the  velocities  of  the  molecules  are  increased 
by  the  attractive  forces,  which,  of  course,  increase  the  temperature  of  the  mass.  This 
increase  in  temperature  must  be  counteracted  by  the  withdrawal  of  heat.  The  energy 
developed  by  the  movement  of  the  molecules  under  these  attractive  forces  is  the  latent 
heat  of  evaporation  of  the  liquid. 

Since  all  of  the  molecules  do  not  have  the  same  velocity,  and  the  distribution  of 
velocities  among  the  molecules  is  determined  by  the  laws  of  chance,  it  follows  that  the 
pressure  at  which  condensation  occurs,  for  a  given  temperature,  does  not  necessarily 
correspond  to  any  particular  point  upon  the  isothermal  of  the  vapor,  but  is  determined 
by  the  distribution  of  the  velocities.  It  may  therefore  be  shown  that  the  relation 
between  the  pressure  and  temperature  of  vaporization  of  any  vapor  may  be  expressed 
by  an  equation  of  the  form 

(29) 


It  may  also  be  pointed  out  that  the  temperature  of  condensation  for  a  given  pressure 
is  independent  of  the  mass  of  the  vapor  considered  and  of  the  form  of  the  containing 
vessel,  since  this  condensation  is  due  to  the  concentration  of  molecules  at  local  points 
and  is  not  due  to  the  simultaneous  concentration  of  the  whole  mass  of  vapor  by  the  sum 
total  of  all  the  attractive  forces. 

368.  The  Phenomena  of  Vaporization.  The  molecules  of  a  liquid  may  be  assumed 
to  be  in  constant  agitation  in  the  same  way  as  are  those  of  a  gas.  In  the  case  of  a 
liquid,  however,  the  molecules  are  restrained  from  leaving  the  mass  freely  on  account 
of  their  attraction  for  one  another,  If  the  surface  of  a  liquid  be  assumed  to  be  in  con- 
tact with  its  own  vapor,  the  surface  of  the  liquid  will  be  continually  struck  by  mole- 
cules of  the  vapor.  In  order  that  the  liquid  shall  not  continually  gain  in  mass,  it  is 
necessary  to  assume  that  when  the  the  liquid  and  vapor  are  in  thermal  equilibrium 
(i.e.,  when  they  have  the  same  temperature)  the  number  of  molecules  leaving  a  given 
area  of  the  liquid  in  a  given  time  is  equal  to  the  number  of  molecules  of  the  vapor 
striking  this  surface  in  the  same  time.  The  molecules  which  leave  the  liquid  are 
necessarily  those  which  have  a  superior  velocity.  Consequently,  when  a  liquid  suffers 
the  loss  of  some  of  its  molecules  by  being  in  contact  with  a  mass  of  its  vapor  whose 
saturation  temperature  is  lower  than  the  temperature  of  the  liquid,  those  particles  which 
leave  the  liquid  (i.e.,  which  are  evaporated),  are  those  having  superior  velocity.  Con- 
sequently, by  the  evaporation  of  some  of  its  particles,  the  temperature  of  the  liquid 
will  be  lowered.  In  escaping  from  the  liquid,  the  particles  lose  that  portion  of  their 
kinetic  energy  which  is  expended  in  separating  them  from  the  remainder  of  the  mass 
of  liquid,  against  the  attractions  of  the  molecules  of  tne  liquid. 

In  the  case  of  a  sensibly  perfect  gas,  the  number  of  molecules  which  strike  a  given 
surface  in  a  given  time  is  proportional  to  the  number  of  molecules  per  unit  of  volume 
and  also  to  the  velocity  of  the  molecules.  From  the  characteristic  equation  of  gases 
we  may  write 

W         P 

V-tt      ...........     (30) 

W 
in  ;  which  ^  is  proportional  to  the  number  of   molecules  per   unit  of  volume.     The 

mean  velocity  of  the  molecules  is  proportional  to  the  square  root  of  the  absolute  tem- 
perature, so  that  the  molecules  striking  upon  a  given  surface  in  a  given  time,  in  the 
case  of  a  sensibly  perfect  gas,  is  proportional  to  the  pressure  of  the  gas  divided  by 


.402  THE   KINETIC  THEORY   OF  HEAT  ART.  369 

-  the  square  root  of  its  absolute  temperature.  In  the  case  of  a  vapor,  the  number 
of  molecules  striking  a  given  area  of  the  surface  of  a  liquid  in  a  given  time  is  nearly 
proportional  to  the  pressure  of  the  vapor,  so  that  the  rate  of  evaporation  from  the  sur- 
face of  a  liquid  is  nearly  proportional  to  the  vapor  pressure  corresponding  to  the  tem- 
perature of  the  liquid.  Hence,  when  the  surface  of  a  liquid  is  in  contact  with  a  gaseous 
medium  in  which  the  pressure  of  its  vapor  is  less  than  the  saturation  pressure  correspond- 
ing to  the  temperature  of  the  liquid  (as,  for  instance,  when  a  body  of  warm  water  is 
exposed  to  cold  air),  the  rate  of  evaporation  from  the  surface  of  the  liquid  is  nearly 
proportional  to  the  difference  between  the  pressure  of  the  vapor  and  the  vapor  pressure 
corresponding  to  the  temperature  of  the  liquid. 

369.  Diffusion  of  Gases.     On  account  of  the  attraction  which  the  molecules  of  a  gas 
have  for  one  another,  they  do  not  pass  from  point  to  point  in  straight  lines,  but  through 
the  influence  of  the  neighboring  molecules,  the  directions  of  their  paths  are  being  con- 
tinually changed.    On  this  account,  a  molecule,  although  it  has  a  high  velocity,  is  very 
slow  in  moving  from  point  to  point. 

If  two  gases  be  separated  from  one  another  by  an  imaginary  surface,  the  molecules 
of  one  gas  will  tend  to  pass  between  those  of  the  other  gas  and  the  two  will  mix,  the 
process  being  known  as  diffusion.  However,  the  progress  of  the  molecules  is  slow 
on  account  of  the  inter-molecular  attractions,  so  that  diffusion  is  a  gradual  and  com- 
paratively slow  process.  The  higher  the  velocity  of  the  molecules,  the  faster  will  be 
the  rate  at  which  they  diffuse  into  one  another,  so  that  at  high  temperatures,  gases 
diffuse  faster  than  at  low  temperatures  and  light  gases  diffuse  faster  than  do  heavy 
ones.  On  the  other  hand  diffusion  is  retarded  by  high  pressures. 

Vapors  diffuse  through  gases  in  the  same  way  as  do  other  gases.  Consequently, 
if  a  gas  be  in  contact  with  a  liquid,  the  evaporation  of  the  liquid  will  cause  its  vapor 
to  diffuse  into  the  gas.  The  pressure  of  the  vapor  in  contact  with  the  liquid  will  be 
very  nearly  the  pressure  of  the  gas,  in  case  the  temperature  of  the  liquid  is  such  that 
the  saturation  pressure  of  its  vapor  is  equal  to  or  greater  than  that  of  the  gas.  In  case 
it  is  less  than  the  pressure  of  the  gas,  the  pressure  of  the  vapor  in  contact  with  the 
liquid  will  be  very  nearly  the  saturation  pressure  corresponding  to  the  temperature  of 
the  gas.  By  the  continual  diffusion  of  the  vapor  into  the  gas,  the  pressure  of  the 
vapor  in  contact  with  the  liquid  will  become  a  trifle  lower  than  the  saturation  pressure 
at  the  temperature  of  the  gas. 

This  accounts  for  the  phenomena  of  evaporation  in  air  which  is  not  saturated  with 
moisture.  If  a  surface  of  water  be  exposed  to  air  of  the  same  temperature,  the  water 
will  evaporate  and  the  air  in  contact  with  the  water  will  become  saturated  with  water 
vapor.  This  water  vapor  will  diffuse  away,  lowering  the  vapor  pressure  sufficiently 
to  permit  of  more  evaporation.  The  temperature  of  the  water  will  fall,  on  account 
of  this  evaporation,  until  finally  equilibrium  is  established,  and  the  rate  at  which  the 
water  receives  heat  by  radiation  and  conduction  from  surrounding  objects  will  become 
equal  to  the  rate  at  which  it  parts  with  heat  by  evaporation.  The  pressure  of  the 
water  vapor  in  the  air  in  contact  with  the  water  will  then  be  slightly  lower  than  the 
saturation  pressure  corresponding  to  the  temperature  of  the  water.  The  rate  of 
evaporation  will  then  depend  upon  the  humidity  of  the  air  and  the  rate  of  diffusion 
of  the  water  vapor,  in  case  the  air  is  still.  In  case  there  is  a  wind,  the  process  is  greatly 
accelerated. 

370.  Dissociation  of  Gases.    It  has  already  been  pointed  out  that  the  atoms  which 
constitute  a  molecule  have  motion  relative  to  one  another  and  that,  in  consequence, 
the  gas  has  intra-molecular  energy.     As  the  temperature  of  the  gas  is  increased,  its 
intra-molecular  energy  is  also  increased.     It  is  reasonable  to  assume  that  the  internal 
energy  of  a  molecule  is  due  to  the  rotation  of  its  several  atoms  about  their  common 
center  of  attraction,  exactly  as  the  bodies  of  the  solar  system  revolve    about  their 


ART.  371         VARIATION  OF  THE  SPECIFIC  HEATS  OF  GASES  403 

common  center  of  attraction,  under  the  influence  of  gravitation.  So  long  as  such  a 
system  of  atoms  is  unacted  upon  by  an  external  force  the  sum  of  the  potential  and  kine- 
tic energies  of  the  system  remains  constant  and  the  system  remains  a  unit.  If  some 
external  force,  (e.g.,  a  collision  with  another  molecule),  increases  the  sum  of  the  potential 
and  kinetic  energy  of  the  system  to  some  value  greater  than  the  potential  energy 
which  the  system  would  have  were  its  several  atoms  removed  to  an  infinite  distance 
from  one  another,  the  system  is  permanently  broken  up  and  thereafter  consists  of  two 
or  more  separate  atoms.  If  any  of  these  atoms  then  encounters  another  atom  upon 
which  it  can  exert  an  attraction,  the  two  would  combine  to  form  a  new  system,  pro- 
vided their  initial  relative  velocity  is  not  such  as  to  prevent. 

In  a  gas,  the  internal  energy  of  most  of  the  molecules  is  very  nearly  the  mean  of 
that  of  all  the  molecules.  A  few  of  the  molecules,  however,  will  have  internal  energies 
greater  in  excess  of  the  mean  value  and  the  energies  of  some  of  these  will  be  so  great 
that  the  molecules  will  be  disintegrated.  As  the  temperature  of  the  gas  is  raised,  the 
number  of  molecules  so  broken  up  will  be  increased  until  finally  a  sufficient  number 
of  them  are  so  separated  that  their  presence  has  an  appreciable  effect  upon  the  prop- 
erties of  the  gas.  This  phenomenon  is  termed  dissociation. 

If  two  gases  capable  of  forming  a  chemical  compound  are  mixed  together,  they 
will  not  usually  react  with  one  another.  Occasionally,  however,  a  molecule  of  one 
gas  will  be  broken  up  and  the  separate  atoms,  meeting  separate  atoms  of  the  other  gas, 
combine  with  them  to  form  a  molecule  of  the  compound.  The  formation  of  the  com- 
pound at  ordinary  temperature  progresses  with  very  great  slowness,  since  the  number 
of  dissociated  molecules  is  very  small.  If  the  temperature  be  sufficiently  raised,  how- 
ever, so  that  an  appreciable  number  of  the  molecules  of  either  of  the  gases  are  dis- 
sociated, the  reaction  will  become  more  rapid.  When  it  becomes  so  rapid  that  heat  is 
generated  by  the  reaction  at  a  faster  rate  than  it  is  radiated,  the  kindling  point  of 
the  mass  is  reached,  since  the  increase  in  temperature  then  accelerates  the  reaction, 
and  the  reaction  in  turn  accelerates  the  increase  in  temperature,  and  the  reaction 
is  thereafter  self-sustaining. 

The  generation  of  heat  by  the  reaction  will  raise  the  temperature  of  the  whole  mass 
of  gas.  As  a  result  of  this  increase  in  temperature,  some  of  the  compound  will  be  dis- 
sociated. At  the  temperature  which  results  from  the  reaction  a  very  considerable 
proportion  of  the  compound  is  thus  dissociated,  so  that  the  full  amount  of  the  heat  of 
combustion  is  not  immediately  developed  by  the  reaction.  This  is  the  phenomenon 
spoken  of  in  Chapter  XX  as  delayed  combustion.  As  the  gas  cools  by  radiation  and 
conduction,  the  number  of  molecules  containing  more  than  the  limiting  quantity  of 
internal  energy  will  be  reduced,  and  the  remainder  of  the  heat  of  combustion  will  be 
evolved,  until  at  ordinary  temperatures  practically  none  of  the  molecules  of  the  com- 
pound are  dissociated. 

371.  Variation  of  the  Specific  Heats  of  Gases.  The  effect  of  the  dissociation  of  a 
gas  at  high  temperatures  is,  of  course,  to  change  the  nature  of  the  gas.  It  also  changes 
the  apparent  specific  heat  of  the  gas  by  increasing  it.  Since  the  number  of  molecules 
is  increased  (on  account  of  the  separate  atoms  becoming  molecules)  the  pressure  and 
volume  of  the  gas  at  a  given  temperature  is  also  increased. 

At  low  temperatures  a  gas  confined  at  constant  volume  has  a  constant  specific 
heat.  If,  however,  the  gas  be  confined  at  constant  pressure,  the  specific  heat  will  be 
found  to  vary,  since,  as  the  volume  diminishes,  a  portion  of  the  potential  energy  which 
resides  in  the  gas  in  virtue  of  the  attraction  of  its  molecules  is  given  up  in  the  form 
heat.  As  the  volume  of  the  gas  diminishes,  the  strength  of  the  attractive  forces  increases, 
and  the  amount  of  potential  energy  transformed  into  heat  by  a  given  temperature 
reduction  also  increases.  Consequently,  in  the  case  of  an  imperfect  polytomic  gas, 
the  specific  heat  at  constant  volume  increases  gradually  as  its  temperature  is  raised, 


404  THE    KINETIC    THEORY  OF  HEAT  ART.  371 

and  the  specific  beat  at  constant  pressure  at  first  decreases  and  then  afterward  increases 
as  the  temperature  is  raised.  The  variation  in  the  specific  heat  at  constant  pressure 
of  permanent  gases  having  a  high  dissociation  temperature  will,  however,  be  so  small 
at  ordinary  temperatures  as  to  defy  measurement.  In  the  case  of  monatomic  gases, 
there  will  be  no  variation  in  the  specific  heat  at  high  temperatures,  since  there  can 
be  no  dissociation  of  such  gases.  It  follows  that  a  constant  pressure  thermometer 
using  a  monatomic  gas  as  its  thermometric  fluid,  will  give  results  which  agree  perfectly 
with  the  thermodynamic  scale  of  absolute  temperatures,  except  for  the  accidental 
errors  of  the  instrument  itself.  It  is  to  be  regretted,  therefore,  that  hydrogen  and  not 
helium  was  chosen  as  the  thermometric  fluid  in  the  standard  thermometer,  although 
at  ordinary  temperatures,  it  is  quite  probable  that  the  indications  of  the  hydrogen 
thermometer  are  so  exact  that  the  errors  resulting  from  dissociation  are  completely 
masked  by  the  accidental  errors  of  the  instrument  itself. 


INDEX 


Absolute  pressure,  4. 

Absolute  temperature  of  gases,   14,  393, 
394. 

Absolute  zero,  14. 

Absorption  system  of  refrigeration,  351. 

Absorption   system   of   refrigeration,    en- 
tropy diagram,  389. 

Atmosphere  of  planets,  397. 

Atmosphere,  pressure  of,  3. 

Acetylene,  336. 

Action  of  steam  in  compound  engines,  162. 

Actual  form  of  card  from  a  steam  engine, 
104. 

Adiabatic  expansion  of  gases,  25,   29,   31, 

396. 
"     ,  work  of,  32. 

Adiabatic  expansion  line,  construction  of, 
33. 

Adiabatic   expansion   of   vapors,    79,    81. 

Adiabatics  on  the  entropy  diagram,  368. 

Advantages  of  multiple  expansion,  162. 

After  burning  in  gas  engines,  305. 

Air  compressors,  332,  333. 

,  design  of,  339. 
,  entropy  diagram,  389. 
"        ,  multistage,  334. 

Air  engines,  274. 

Air  leakage,  effect  of,  on  boiler  efficiency, 
243. 

Air  in  the  condenser,  208. 

Air,  moist,  properties  of,  94. 

Air  pump,  199,  209. 

Air  refrigerating  machines,  346. 

,  entropy     dia- 
gram, 389. 

Air  required  for  ventilation,  356. 

Alternate  method  of  firing,  230. 

Altitude,   effect  of,   on  air    compressors, 
337. 

Ammonia  compression  machines,  349,  350, 

Ammonia  compression  machines,  entropy 
diagram,  389, 


Analysis  of  nue  gas,  218. 
Analysis  of  gas  engine  test,  313. 
Analysis   of   losses   in   steam    engine   by 

entropy  diagram,  380. 
Analysis  of  steam  engine  tests,  171,  174. 
Angle  compound  engine,  159. 
Anthracite  in  gas  producers,  328 
Area,  unit  of,  3. 

Arrangements  of  cylinders  of  engines,  159. 
Augmentor  condenser,  209. 
A  very  turbine,  178. 

Balanced  slide-valves,  111 
|    Barometric  condensers,  207. 
Barrel  calorimeter,  84. 
Bearings,  design  of,  153. 
Beau  de  Rochas  cycle,  285. 
Bench  gas,  320. 

Bituminous  coal  in  gas  producers,  328. 
Blowing  engines,  338. 
Blast  furnace  gas,  330. 
Body,  defined,  51. 
Boiler  efficiency,  conditions  of,  241. 
Boiler  horse-power,  240. 
Boiler,  theory  of,  237. 
Boyle's  Law,  12. 
Bridge  wall,  232. 
British  thermal  unit,  7. 
B.T.U.,  7. 
By-product  coke  oven  gas,  321. 

Calibration  of  orifices,  46. 
Calorimeter,  Parr's,  222. 
Calorimeters,  steam,  81. 
Capacity  of  air  compressors,  337. 
Capacity  of  refrigerating  plants,  353. 
Carbon,  combustion  of,  215,  216. 
Carbon  dioxide  in  ventilation,  356. 
Carburetors,  311. 
Card  factor,  144. 
Cards,  air  compressor,  333. 
' '     ,  gas  engine,  304. 

405 


406 


INDEX 


Cards,  steam  engine  indicator.     See  The- 
oretical and  Actual. 
Carnot  air  engines,  274. 
Carnot  cycle,  56,  57,  58. 
Carnot  cycle  for  steam,  125,  126. 
Carnot  cycle  on  the  temperature-entropy 

diagram,  373. 

Centigrade  thermometer  scale,  6. 
Centrifugal  feed  pumps,  259. 
Chain-grate  stoker,  227. 
Characteristic  equation  of  gases,  15. 
Chimneys,  height  of,  252. 

"        ,  overload  capacity,  256. 

,  diameter  of,  255. 
Circulating  pumps,  199. 
Clausius'  equation,  399. 
Clausius'  ratio,  396. 
Cleaning  of  air  for  ventilation,  363. 
Cleaning  of  fires,  230. 
Clearance,    effect    of   in    steam    engines, 

136. 

' '       ,  loss  from  in  steam  engines,  153. 
' '       ,  effect  of  in  air  compressors,  337. 
Clinkers,  330. 

Clinkers  in  gas  producers,  328. 
Closed  heaters,  260. 
Coal,  combustion  of,  223. 

' '    ,  composition  of,  222.. 
Coal  gas,  320. 
Coal,  heating  value  of,  222. 
Coal  in  gas  producers,  328. 
Coking  method  of  firing,  230. 
Coke  oven  gas,  321. 
Combined   cards  for  multiple  expansion 

engines,  170. 
Combustion,  214. 
Combustion  chamber,  232. 
Combustion  of  coal,  223. 
Combustion,  delayed,  402. 

' '        in  gas  engines,  302, 

305. 
,  efficiency  of,  219. 

heat  of,  214. 
' '  rate  of,  240. 

' '  suppressed,  in  gas  engines, 

302,  305. 

Comparative  engine  efficiencies,  174. 
Comparison  of  methods  of  governing,  107. 
Complete  expansion  gas  engine  cycle,  296. 
Compound  engines,  100,  159. 

"  "       action  of   steam    in, 

162. 


Compound  engine, entropy  diagram  for,380. 

Compounds,  combustion  of,  217. 

Compressed  air,  332. 

' '  applications  of,  342. 

Compression,  efficiency  of  in  air  compres- 
sor, 335. 

Compression  in  gas  engines,  302. 

Compression  of  gases,  38. 

Compression,  work  of,  in  air  compressors, 
335. 

Condensation  in  the  cylinder,   144,    146, 
147. 

Condensation,  phenomena  of,  400. 

Condenser  action,  imperfect,  143. 

Condensers,  arrangement  of,  200. 

barometric,  207. 
"          effect  of,  in  air,  208. 
"          ejector,  206. 
jet,  204. 
surface,  199. 

Condensing  engines,  100. 

Conducting  walls,  398. 

Conductivity,    effect    of,    on    boiler   effi- 
ciency, 243. 

Conduction,  loss  from  in  engines,  152. 

Conservation  of  energy,  1. 

Contra-flow  condenser,  200. 

Cooling  ponds,  264. 

Cooling  pond,  area  of,  266. 

Cooling  towers,  268,  269,  270,  271. 

Corliss  engine,  116. 

Corliss  valves,  97. 

double-ported,  116. 

Corliss  valve  motion,  116. 

Critical  state,  76. 

Critical  volume,  76. 

Critical  pressure,  76. 

Cross  compound  engine,  159. 

Curtis  turbine,  187. 

Cut-off  governor,  107. 

Cycle,  Carnot,  56. 
"      defined,  52. 

Cycles,  limits  of  efficiency,  58. 

Cycles  on  the  entropy  diagram,  370. 

Cylinder  arrangements  of  engines,  159. 

Cylinder  condensation,  144,  147-149. 

Cylinder  dimensions  of  compound  engines, 
163. 

DeLaval  turbines,  187. 
Delayed  combustion  a  in  gas  engine,  302, 
305. 


INDEX 


407 


Density  of  vapors,  66. 

Design  of  air  compressors,  339. 

Design  of  gas  engine,  308. 

Dew  point,  93. 

Diameter  of  chimneys,  255. 

Diesel  cycle  engine,  298. 

Diffusion  of  gases,  402. 

Dimensions  of  entropy,  53. 

Direct  heating,  358. 

Discharge  from  an  orifice,  44. 

Dissociation  of  gases,  402. 

Dissociation  in  gas  engines,  302,  305. 

Distillation,  366. 

Dome,  steam,  372. 

Double-beat  poppet  valves,  121. 

Double-effect  evaporators,  365. 

Double-ported  Corliss  valves,  116. 

Down-draft  furnace,  228. 

Draft  produced  by  chimney,  252. 

Draft  required  by  boilers,  253. 

Draft  required  by  overload,  254. 

Driving,  rate  of,  240. 

Drying,  367. 

Dry  vacuum  pump,  191,  209. 

Duplex  compound  engine,  159. 

Dutch  oven  furnace,  227. 

Economizers,  261. 

Efficiency  of  compression  in  air  compres- 
sor, 335. 

Efficiency,  conditions  of  "boiler,  241. 
11       ,  effect  of  load  on  175. 
' '        ,  limits  of,  for  cycles,  58. 
Efficiency  of  combustion,  219. 
Efficiency  of  engines,  comparative,  174. 
Efficiency  of  gas  engines,  315. 
Efficiency  of  heating  surface,  239. 
Efficiency  of  refrigerating  plants,  353. 
Efficiency  of  steam  engines,  100. 
Effective  pressure,  mean,  105. 
Ejector  condenser,  206. 
Elastic  fluids  defined,  12. 
Electric  ignition,  309. 
Energy,  conservation  of,  1. 
Energy  drop  in  multi-stage  turbines,  191. 
Energy,  fundamental  unit  of,  3. 

"       interconvertibility  of,  1. 

' '       internal,  of  evaporation,  67. 

"       internal,  of  steam,  67. 

"       natural  sources  of,  1. 
Engines,  Corliss,  116. 

' '       cost  of,  158. 


Engines,  efficiency  of,  100. 
rotary,  123. 

Entropy  defined,  52. 

Entropy  diagrams,  368-389. 

Entropy,  dimensions  of,  52. 

Entropy  of  evaporation,  67. 

Entropy  of  steam,  67. 

Entropy  of  the  liquid,  67. 

Entropy,  propositions  concerning,  53,  54, 
55,  56. 

Equilibrium,  defined,  51. 

Equilateral  hyperbola,  26. 

Ericsson  hot  air  engine,  282. 

Evaporation,  365. 

Evaporation  from  water,  rate  of,  265. 

Evaporation  on  the  entropy  diagram,  371. 

Evaporation,  phenomena  of,  401. 
' '  rate  of,  240. 

work  of,  67. 

Exhaust  steam  heating,  361. 

Exhaust  lap,  108. 

Expansion,  adiabatic,  25. 
"         ,  isobaric,  25. 
' '         ,  isothermal,  25. 
"         ,  polytropic,  25. 

Expansion  in  gas  engines,  302. 

Explosion  in  gas  engines,  302. 

Explosive    pressure,    velocity    of    trans- 
mission, 40. 

External  work  of  evaporation,  67. 

Factor,  card,  144. 

Fahrenheit  thermometer  scale,  6. 

Feed  pumps,  259. 

Feed-water  heaters,  260. 

Fire-tube  boilers,  234. 

Flash  boiler,  234. 

Flow  of  air  in  tubes,  340. 

Flow  of  gas  through  an  orifice,  41,  397. 

Flue  gas  analysis,  218. 

Flue  gas,  temperature  of,  240. 

Fluids  defined,  12. 

Fluids,  elastic,  defined,  12. 

Foot,  2. 

Foot-pound  second  system,  2. 

Forced  ventilation,  363. 

Force,  unit  of,  3. 

Formation,  heat  of,  214. 

Four-cylinder     triple-expansion     engine, 

159. 

Four-stroke  cycle  engine,  285. 
Four- valve  engine,  119. 


40S 


INDEX 


Freezing  point,  77. 

Friction,  loss  from  steam,  168. 

' '     ,  loss  from  mechanical,  153. 
Fuel  gases,  calssification  of,  320. 
Fusion,  latent  heat  of,  77. 
' '     ,  temperature  of,  77. 

Gage  pressure,  4. 
Gases,  classification  of  fuel,  320. 
"     ,  denned,  12. 
"    ,  diffusion  of,  402. 
' '    ,  dissociation  of,  402. 
Gas  engines,  285. 

behavior  of  charge  in,  302. 
design  of,  308. 
"  efficiency  of,  315. 

' '  entropy  diagram  for,  387. 

' '  governing  of,  292. 

losses  of,  305. 
"'  losses  in,  387. 

"  testing  of,  313. 

two-cycle,  294. 
Gaseous  mixtures,  90. 
Gases  and  vapors,  mixtures  of,  92. 
Gases,  variation  in  specific  heat  of,  403. 
"      liquefaction  of,  352. 
11     kinetic  theory  of,  393. 
"     specific  heats  of,  19. 
Gas  thermometers,  18. 

errors  of,  403. 

Governing,  methods  of,  105. 
Governing  of  gas  engines,  292. 
Governing  of  steam  turbines,  195. 
Governor,  throttling,  106. 
Graphical  analysis  of  engine  test,  171. 
Gravitation,  acceleration  of,  3. 
Grid-iron  valves,  120. 

Hawley  down-draft  furnace,  228. 
Heat  drop  in  multi-stage  turbines,  191. 
Heaters  for  feed-water,  260. 
Heat,  effects  of,  4. 
Heat  engine,  52. 
Heating,  direct,  358. 

' '       ,  indirect,  363. 

11      ,  hygiene  of,  356. 
Heating  surface,  efficiency  of,  239. 
Heating,  systems  of,  358. 
Heating  value  of  coal,  222. 
Heat,  mechanical  equivalent  of,  222. 
Heat  of  formation,  214. 
Heat  of  combustion,  214. 


Heat  of  the  liquid,  66. 

Heat  on  the  entropy  diagram,  368. 

Heat  required  for  heating  and  ventila- 
tion, 358. 

Heat,  specific,  8. 

Heat  transmission,  rate  of,  in  condensers, 
203. 

Horizontal  water  tube  boilers,  233. 

Horizontal  return  tubular  boiler,  232. 

Horse-power  of  a  boiler,  240. 

Hot  air  engine,  274. 

Carnot,  274. 
.    Ericsson,  282. 

Joule,  276. 
"  Stirling,  278. 

Hot  air  engines,  entropy  diagrams  for,  386. 

Hot  tube  igniter,  309. 

Hot  water  heating,  362. 

Humidity  of  air,  93,  94, 

Humidity  of  air  used  in  ventilation,  356. 

Hydrogen,  combustion  of,  217. 

Hydrogen  thermometers,  18. 

Hygiene  of  heating  and  ventilation,  356. 

Hygrometer,  wet  bulb,  93. 

Hyperbola,  equilateral,  26. 

Ice-melting  effect,  353. 

Ignition,  methods  of  gas  engine,  309. 

Illuminating  gas,  320. 

Imperfect  condenser  action,  143. 

Imperfect     cycle     on     the     temperature- 
entropy  diagram,  373. 

Imperfect  cycles,  134,  52. 

Imperfect  gases,  properties  of,  391. 

Impulse  reaction  turbines,  193. 

Indicator,  101. 

Indicator  card,  25. 

Indicator  card  from  steam  engine,  103. 

Indicator  card  transferral  to  temperature- 
entropy  plane,  381. 

Indicator  card.     See     Theoretical  and 
Actual. 

Indirect  heating,  363. 

Injector,  257. 

Internal  combustion  engines,  285. 

Internal  combustion  engine,see  Gas  engine. 

Internal  energy  of  evaporation,  67. 

Internal  energy  of  steam,  67. 

Intra-molecular  energy,  396. 

Intrinsic  energy  of  a  gas,  22. 

Irreversible  processes,  511. 

Isobaric  expansion,  25,  35. 


INDEX 


409 


Isothermal  expansion,  25. 
Isothermal  expansion  of  vapor,  78. 
Isothermal  expansion,  work  of,  26. 
Isothermals  on  the  entropy  diagram,  368. 

Jacket,  design  of,  166. 
Jacketed  cycle,  131. 

entropy  diagram  of,  373. 
Jet  condenser,  204. 
Joule  cycle  reversed  for  refrigeration,  346, 

347. 

Joule  engine,  entropy  diagram  of,  386. 
Joule  hot  air  engine,  276. 
Joule-Thompson  effect,  22. 
Jump  spark  ignition,  309. 

Kerr  turbine,  178. 
Kilns  for  drying,  367. 
Kilogram,  2. 
Kindling  point,  402. 
Kinetic  mass  unit,  3. 
Kinetic  theory  of  gases,  393. 

Latent  heat,  67. 
Lap,  108. 

Leakage,  effect  of  air,  on  boilers,  243. 
"       ,  effect  on    compression     in    gas 

engines,  379. 

Leakage  in  steam  engines,  151. 
Length,  units  of,  2. 

Limits  of  condensation  temperature,  142. 
Limits  of  steam  pressure  and  superheat, 

141. 

Link  motion,  113. 
Liquefaction  of  gases,  352. 
Liquefaction,  phenomena  of,  400. 
Liquids  denned,  12. 
Liquid,  heat  of,  66. 
Load  curve,  form  of,  175. 
Load,  effect  of,  on  efficiency,  175. 
Locomotove  boiler,  234. 
Losses  in  boiler  plants,  246. 
Losses  in  gas  engines,  305,  313. 
Losses  in  gas  engines,  on  entropy  diagram, 

387. 

Losses  in  steam  engines,  141. 
Losses    in    steam    engines,    on    entropy 

diagram,  380. 

Make  and  break  spark  ignition,  309. 
Management  of  fires,  230. 
Marine  boiler,  234. 


Mass  unit,  kinetic,  3. 

Mass,  units  of,  2. 

Mclntosh-Seymour  engine,  120. 

Mean  effective  pressure,  105. 

Mechanical  equivalent  of  heat,  7 

Mechanical  stoker,  227. 

Melting  point,  77. 

Mercury  thermometers,  7. 

Meter,  2. 

Mining,  pneumatic  tools  for,  341. 

Mixtures  of  gases  and  vapors,  92. 

Moist  air,  properties  of,  94. 

Moisture  in  compressed  air,  339. 

Mollier's  diagram,  384. 

Multiple  expansion,  advantages  of,  000. 

Multiple     expansion     engines,     cylinder 

arrangements,  159. 
Multi-ported  slide  valves,  111. 
Multi-stage  air  compressor,  334. 
Multi-stage  turbines,  187. 

Natural  gas,  323. 
Natural  sources  of  energy,  1. 
Negative  lap,  108. 
Non-condensing  engines,  100. 
Nozzles,  design  of  steam,  183. 

' '        efficiency  of  steam,  186; 

"        form  of  steam,  181. 

' '        theory  of  steam,  178. 

Open  heaters,  260. 
Orifice,  discharge  from,  44. 

"      flow  of  gas  through,  41. 
Orifices,  calibration  of,  46. 
Orsat  apparatus,  218. 
Osmosis,  398. 
Otto  cycle,  286,  290. 
Otto  cycle  engine,  285. 

1 '       ,  Actual  entropy  diagram 

for,  302. 
' '  ' '        ,  entropy     diagram    for 

387. 

Overload,  effect  upon  capacity  of    chim- 
ney, 256. 

Parker  boiler,  234. 
Parr's  calorimeter,  222. 
Parsons'  turbine,  193. 
Perfect  cycle,  52. 
Perfect  gas  defined,  16. 
Physical  states  of  matter,  12. 
Pipes,  flow  of  air  in,  340. 


410 


INDEX 


Piston  valves,  111. 

Pneumatic  riveters,  341. 

Pneumatic  tools,  341. 

Polytropic  expansion,  25,  37. 

Polytropics  on  the  entropy  diagram,  368. 

Ponds  for  cooling  condensing  water,  264. 

Poppet-valves,  121. 

Ports,  design  of,  144. 

Positive  lap,  108. 

Pound,  2,  3. 

£ower  of  an  engine,  105. 

Power,  unit  of,  3. 

Practical  cycle  for  steam  engine,  137,  138. 

Preheating  air  for  air  motors,  341. 

Pressure,  absolute,  4. 

Pressure  drop  in  multi-stage  turbine,  191. 

Pressure  gage,  4. 

Pressure  gas  producers,  327. 

Pressure  of  gases,  cause  of,  393. 

Pressure,  units  of,  3. 

Pressure  volume  diagram,  25. 

Process,  defined,  51. 

Producer  gas,  324. 

Properties  of  imperfect  gases,  399. 

Properties  of  steam,  68,  69. 

Properties  of  superheated  vapors,  74. 

Properties  of  wet  vapor,  72. 

Pseudo-cycles,  62. 

PV  diagram,  25. 

Quadruple  expansion  engines,  100. 

Quality  of  a  vapor,  81. 

Quarrying,  pneumatic  tools  for,  341. 

Radiation,  effect  of,  on  boiler  efficiency,244. 

' '        loss  from,  in  steam  engines,  152. 

Radiation    surface   required   for   heating 

rooms,  351,  387. 
Rankine  cycle,  127,  129. 
Rankine  cycle  on  the  temperature-entropy 

diagram,  373 . . 
Rankine  jacketed  cycle,  131. 
Rate  of  driving,  effect  of,  242. 
Ratio  of  the  specific  heats  of  gases,  395, 396. 
Reaction  turbine,  193. 
Receivers,  design  of,  165. 
Refrigerating  machines,  52,  346,  347,  349, 

350. 
,  entropy  diagram, 

389. 

Refrigerating  plants,  capacity  of,  353. 
' '  efficiency  of,  353. 


Refrigeration,  345. 
Regenerator,  61. 
Return-tubular  boiler,  232. 
Reversible  process,  51. 
Riding  cut-off,  112. 
Riveters,  pneumatic,  341. 
Rocking-grate  stoker,  227. 
Rotary  engines,  123. 

Sargent  cycle,  entropy  diagram  for,  387. 

Sargent  gas  engine  cycle,  296. 

Scale  'of  indicator  springs,  101. 

Scotch  boiler,  234. 

Second,  3. 

Separating  calorimeter,  84. 

Separators,  86. 

Simple  engines,  100. 

Single-stage  turbines,  187. 

Slide-valves,  108. 

11  defects  of,  110. 

"  multi-ported,  111. 

Smoke,  prevention  of,  224,  225. 

Solids,  defined,  12. 

Sound,  velocity  of,  38. 

Sources  of  energy,  1. 

Spark  ignition,  309. 

Specific  heat,  8. 

Specific  heats  of  gases,  19. 

Variation  of,  403. 

Specific  volume  of  vapors,  66. 

Speed  of  gas  engines,  307. 

Spray  ponds,  267,  268. 

State,  defined,  51. 

States,  physical,  12. 

Steam  boilers,  232. 

Steam  calorimeters,  81. 

Steam  cycles  on  the  temperature-entropy 
diagram,  373. 

Steam  dome,  372. 

Steam  engine,  97. 

temperature-entropy     dia- 
gram for,  379. 
testing  of,  171. 

Steam  heating,  358. 

Steam  lap,  134. 

Steam  turbine,  temperature-entropy  dia- 
gram for,  382. 

Still,  366. 

Stirling  boiler,  234. 

Stirling  engine,  entropy  diagram  for,  386. 

Stirling  hot  air  engine,  278. 

Stokers,  mechanical,  227,  228. 


INDEX 


411 


Sublimation,  77. 

Suction  gas  producers,  327. 

Superheated  vapors,  74. 

Superheaters,  262. 

Superheating  on  the  entropy  diagram,  371. 

Suppressed  combustion  in  a  gas  engine, 

302,  305. 
Surface  condensers,  199. 

theory  of,  201. 
Sweeping  process,  51. 
System,  defined,  51. 

Tail  pipe,  206,  207. 
Tandem  compound  engine,  159. 
Tar  in  gas  producers,  328. 
Temperature,  definitions  of,  4. 
Temperature-entropy  diagrams,  368,  392 
Temperature-entropy  lines,  368. 
Temperature,  measurements  of,  5. 
Temperature  of  vaporization,  65. 
Temperature   suitable   for   living   rooms, 

356. 

Testing  of  steam  engines,  171. 
Theoretical   indicator   card   for   multiple 

expansion  engines,  166. 
Theory  of  the  steam  boiler,  237. 
Theoretical  card  for  steam  engines,  103. 
Thermal  equilibrium  of  gases,  397. 
Thermal  unit,  7. 
Thermo-couple,  60. 
Thermodynamics,  defined,  1. 
Thermometer  scales,  6. 
Thermometer,  errors  of  gas,  403. 
Thermometers,  gas,  18. 

mercury,  7. 

Three-cylinder  compound  engine,  159. 
Throttling  calorimeter,  81,  82. 
Throttling  governing,  106. 
Time,  unit  of,  3. 
Total  heat,  69. 

Total  heat-entropy  diagram,  384. 
Triple  effect  evaporators,  365. 
Triple  expansion  engines,  100. 
Tubes,  flow  of  air  in,  340. 
Turbine  nozzle,  efficiency  of,  186. 

form  of,  181. 
' '    •          theory  of,  178. 
Turbines,  efficiency  of,  196. 

' '       governing  of,  195. 
multi-stage,  187. 

"       single-stage,  187. 
Two-cycle  gas  engines,  294. 


Types  of  engines,  158. 
Underfeed  stoked,  228. 

Vacuum  augmentor,  209. 

Valve  gear,  Waalschert,  116. 

Valve  leakage,  151. 

Valve  motion,  Corliss,  116. 

Valve,  Corliss,  97. 

Valves  for  air  compressors,  338. 

Valves,  slide,  108. 

Van  der  Waal's  equation,  399. 

Vanes,  design  of,  186,  189. 

Vapor  absorption  system  of  refrigeration, 
351. 

Vapor  compression  system  of  refrigera- 
tion, 349. 

Vapor,  formation  of,  64. 

Vaporization,  phenomena  of,  401. 
temperature  of,  65. 

Vapors  and  gases,  mixtures  of,  92. 

Vapors,  defined,  12. 
' '       density  of,  66. 
"      diffusion  of,  402. 

Velocity  of  sound,  38. 

Velocity    of    transmission    of    stress    in 
gases,  38,  40. 

Velocity  of  turbine  vanes,  187. 

Ventilation  by  purified  air,  363. 

Ventilation,  hygiene  of,  356. 
,  mechanical,  363. 

Vital  processes,  60. 

Volume,  specific,  of  vapors,  66. 

Volumetric  efficiency  of  air  compressors, 
337. 

Volume,  unit  of,  3. 

Waelschert  valve  gear,  116. 

Water-gas,  322,  323. 

Water-tube  boilers,  233,  234. 

Welsbach  lamp,  322. 

Wet-bulb  hygrometer,  93. 

Wet  vapors,  properties  of,  72. 

Wire  drawing,  loss  from,  143. 

Work  of  compression  in  air  compressor, 

335. 

Wolff  compound  engine,  159. 
Work  of  evaporation,  external,  67. 
Worm,  366. 
Watt  diagram,  25. 

Zero,  absolute,  14. 


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